المؤلفون: Dalík, Josef

مصطلحات موضوعية: keyword:superconvergence, keyword:finite element method, msc:65N30

وصف الملف: application/pdf

الاتاحة: http://hdl.handle.net/10338.dmlcz/702707

المؤلفون: Ludwig, Lars, Roos, Hans-Görg

مصطلحات موضوعية: keyword:singular perturbation, keyword:finite element method, keyword:convection-diffusion boundary value problem, keyword:superconvergence, keyword:supercloseness, msc:35B25, msc:35J25, msc:65N12, msc:65N15, msc:65N30

وصف الملف: application/pdf

Relation: mr:MR3204410; zbl:Zbl 1313.65292

الاتاحة: http://hdl.handle.net/10338.dmlcz/702903

المؤلفون: Huang, Pengzhan

مصطلحات موضوعية: keyword:Stokes eigenvalue problem, keyword:stabilized method, keyword:lowest equal-order pair, keyword:projection method, keyword:superconvergence, msc:65B99, msc:65N25, msc:65N30, msc:76D07

وصف الملف: application/pdf

Relation: mr:MR3233549; zbl:Zbl 06362233; reference:[1] Bochev, P., Dohrmann, C. R., Gunzburger, M. D.: Stabilization of low-order mixed finite elements for the Stokes equations.SIAM J. Numer. Anal. 44 (2006), 82-101 (electronic). Zbl 1145.76015, MR 2217373, 10.1137/S0036142905444482; reference:[2] Chen, H., Jia, S., Xie, H.: Postprocessing and higher order convergence for the mixed finite element approximations of the Stokes eigenvalue problems.Appl. Math., Praha 54 (2009), 237-250. Zbl 1212.65431, MR 2530541, 10.1007/s10492-009-0015-7; reference:[3] Chen, W., Lin, Q.: Approximation of an eigenvalue problem associated with the Stokes problem by the stream function-vorticity-pressure method.Appl. Math., Praha 51 (2006), 73-88. Zbl 1164.65489, MR 2197324, 10.1007/s10492-006-0006-x; reference:[4] Chen, H., Wang, J.: An interior estimate of superconvergence for finite element solutions for second-order elliptic problems on quasi-uniform meshes by local projections.SIAM J. Numer. 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L.: Numerical investigations on several stabilized finite element methods for the Stokes eigenvalue problem.Math. Probl. Eng. 2011 (2011), Article ID 745908, pp. 14. Zbl 1235.74286, MR 2826898; reference:[10] Huang, P. Z., He, Y. N., Feng, X. L.: Two-level stabilized finite element method for Stokes eigenvalue problem.Appl. Math. Mech., Engl. Ed. 33 (2012), 621-630. Zbl 1266.65192, MR 2978223, 10.1007/s10483-012-1575-7; reference:[11] Huang, P. Z., Zhang, T., Ma, X. L.: Superconvergence by $L^2$-projection for a stabilized finite volume method for the stationary Navier-Stokes equations.Comput. Math. Appl. 62 (2011), 4249-4257. Zbl 1236.76017, MR 2859980, 10.1016/j.camwa.2011.10.012; reference:[12] Jia, S., Xie, H., Yin, X., Gao, S.: Approximation and eigenvalue extrapolation of Stokes eigenvalue problem by nonconforming finite element methods.Appl. Math., Praha 54 (2009), 1-15. 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الاتاحة: http://hdl.handle.net/10338.dmlcz/143868

المؤلفون: Zhang, Tie, Zhang, Shuhua

مصطلحات موضوعية: keyword:finite element method, keyword:derivative recovery technique, keyword:superconvergence and ultraconvergence, keyword:elliptic boundary problems, keyword:numerical examples, msc:35J25, msc:65D25, msc:65M60, msc:65N12, msc:65N30

وصف الملف: application/pdf

Relation: mr:MR2886235; zbl:Zbl 1249.65258; reference:[1] Chen, C. M., Huang, Y. Q.: High Accuracy Theory of Finite Element Methods.Hunan Science Press Hunan (1995), Chinese.; reference:[2] Cairlet, P. G.: The Finite Element Methods for Elliptic Problems.North-Holland Publishing Amsterdam (1978).; reference:[3] Hinton, E., Campbell, J. S.: Local and global smoothing of discontinuous finite element functions using a least squares method.Int. J. Numer. Methods Eng. 8 (1974), 461-480. Zbl 0286.73066, MR 0411120, 10.1002/nme.1620080303; reference:[4] Křížek, M., Neittaanmäki, P., (eds.), R. Stenberg: Finite Element Methods. Superconvergence, Postprocessing, and a Posteriori Estimates. Lecture Notes in Pure and Appl. Math., Vol. 196.Marcel Dekker New York (1998). MR 1602809; reference:[5] Lin, Q., Zhu, Q. D.: The Preprocessing and Postprocessing for Finite Element Methods.Shanghai Sci. & Tech. Publishers Shanghai (1994), Chinese.; reference:[6] Oden, J. T., Brauchli, H. J.: On the calculation of consistent stress distributions in finite element applications.Int. J. Numer. Methods Eng. 3 (1971), 317-325. 10.1002/nme.1620030303; reference:[7] Turner, M. J., Martin, H. C., Weikel, B. C.: Further developments and applications of stiffness method.Matrix Meth. Struct. Analysis 72 (1964), 203-266.; reference:[8] Wahlbin, L. B.: Superconvergence in Galerkin Finite Element Methods. Lecture Notes in Mathematics, Vol. 1605.Springer Berlin (1995). MR 1439050; reference:[9] Wilson, E. L.: Finite element analysis of two-dimensional structures.PhD. Thesis University of California Berkeley (1963).; reference:[10] Wang, Z. X., Guo, D. R.: Special Functions.World Scientific Singapore (1989). Zbl 0724.33001, MR 1034956; reference:[11] Zienkiewicz, O. C., Zhu, J. Z.: The superconvergence patch recovery and a posteriori error estimates. Part 1: The recovery technique.Int. J. Numer. Methods Eng. 33 (1992), 1331-1364. MR 1161557, 10.1002/nme.1620330702; reference:[12] Zhang, Z.: Recovery techniques in finite element methods.Adaptive Computations: Theory and Algorithms T. Tang, J. C. Xu Science Press Beijing (2007).; reference:[13] Zhang, Z.: Ultraconvergence of the patch recovery technique II.Math. Comput. 69 (2000), 141-158. Zbl 0936.65132, MR 1680911, 10.1090/S0025-5718-99-01205-3; reference:[14] Zhang, T., Lin, Y. P., Tait, R. J.: The derivative patch interpolation recovery technique for finite element approximations.J. Comput. Math. 22 (2004), 113-122. MR 2027918; reference:[15] Zhang, T., Li, C. J., Nie, Y. Y.: Derivative superconvergence of linear finite elements by recovery techniques.Dyn. Contin. Discrete Impuls. Syst., Ser. A 11 (2004), 853-862. Zbl 1059.65096, MR 2077127; reference:[16] Zhang, T.: Finite Element Methods for Evolutionary Integro-Differential Equations.Northeastern University Press Shenyang (2002), Chinese.; reference:[17] Zhu, Q. D., Meng, L. X.: New structure of the derivative recovery technique for odd-order rectangular finite elements and ultraconvergence.Science in China, Ser. A, Mathematics 34 (2004), 723-731 Chinese.; reference:[18] Zhu, Q. D., Lin, Q.: Superconvergence Theory of Finite Element Methods.Hunan Science Press Hunan (1989), Chinese.

الاتاحة: http://hdl.handle.net/10338.dmlcz/141763

المؤلفون: Yan, Ningning

مصطلحات موضوعية: keyword:optimal control, keyword:integral equation, keyword:Galerkin method, keyword:superconvergence, keyword:a posteriori error estimates, keyword:constrained optimal control problems, keyword:adaptive mesh refinement, msc:49J21, msc:49M25, msc:49M30, msc:65K10, msc:65N30, msc:65R20

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/140364

المؤلفون: Brandts, Jan H.

مصطلحات موضوعية: keyword:least-squares mixed finite element method, keyword:non-standard mixed finite element method, keyword:superconvergence, keyword:supercloseness, msc:35J25, msc:65N12, msc:65N15, msc:65N30

وصف الملف: application/pdf

Relation: mr:MR2530540; zbl:Zbl 1212.65441; reference:[1] Barrios, T. P., Gatica, G. N.: An augmented mixed finite element method with Lagrange multipliers: A priori and a posteriori error analyses.J. Comput. Appl. Math. 200 (2007), 653-676. Zbl 1112.65106, MR 2289241, 10.1016/j.cam.2006.01.017; reference:[2] Bochev, P. B., Gunzburger, M. D.: Finite element methods of least-squares type.SIAM Rev. 40 (1998), 789-837. Zbl 0914.65108, MR 1659689, 10.1137/S0036144597321156; reference:[3] Brandts, J. H.: Superconvergence and a posteriori error estimation for triangular mixed finite elements.Numer. Math. 68 (1994), 311-324. Zbl 0823.65103, MR 1313147, 10.1007/s002110050064; reference:[4] Brandts, J. H., Křížek, M.: Gradient superconvergence on uniform simplicial partitions of polytopes.IMA J. Numer. Anal. 23 (2003), 489-505. Zbl 1042.65081, MR 1987941, 10.1093/imanum/23.3.489; reference:[5] Brandts, J. H., Křížek, M.: Superconvergence of tetrahedral quadratic finite elements.J. Comput. Math. 23 (2005), 27-36. Zbl 1072.65137, MR 2124141; reference:[6] Brandts, J. H., Chen, Y. P.: An alternative to the least-squares mixed finite element method for elliptic problems.In: Numerical Mathematics and Advanced Applications M. Feistauer, V. Dolejší, P. Knobloch, K. Najzar Springer (2004), 169-175. Zbl 1056.65110, MR 2121365, 10.1007/978-3-642-18775-9_14; reference:[7] Brandts, J. H., Chen, Y. P.: Superconvergence of least-squares mixed finite elements.Int. J. Numer. Anal. Model. 3 (2006), 303-310. Zbl 1096.65108, MR 2237884; reference:[8] Brandts, J. H., Chen, Y. P., Yang, J.: A note on least-squares mixed finite elements in relation to standard and mixed finite elements.IMA J. Numer. Anal. 26 (2006), 779-789. Zbl 1106.65102, MR 2269196, 10.1093/imanum/dri048; reference:[9] Brezzi, F.: On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers.Rev. Franc. Automat. Inform. Rech. Operat. 8, R-2 (1974), 129-151. Zbl 0338.90047, MR 0365287; reference:[10] Brezzi, F., Fortin, M.: Mixed and hybrid finite element methods.Springer Berlin-Heidelberg-New York (1991). Zbl 0788.73002, MR 1115205; reference:[11] Cai, Z., Lazarov, R., Manteuffel, T. A., McCormick, S. F.: First-order system least squares for second-order partial differential equations: Part I.SIAM J. Numer. Anal. 31 (1994), 1785-1799. MR 1302685, 10.1137/0731091; reference:[12] Carey, G. F., Pehlivanov, A. I.: Local error estimation and adaptive remeshing scheme for least-squares mixed finite elements.Comput. Methods Appl. Mech. Eng. 150 (1997), 125-131. Zbl 0907.65101, MR 1487940, 10.1016/S0045-7825(97)00098-4; reference:[13] Carey, G. F., Pehlivanov, A. I., Shen, Y., Bose, A., Wang, K. C.: Least-squares finite elements for fluid flow and transport.Int. J. Numer. Methods Fluids 27 (1998), 97-107. Zbl 0904.76043, MR 1602155, 10.1002/(SICI)1097-0363(199801)27:1/43.0.CO;2-2; reference:[14] Ciarlet, P.: The Finite Element Methods for Elliptic Problems. Classics in Applied Mathematics 40. 2nd Edition.SIAM Philadelphia (2002). MR 1930132; reference:[15] Křížek, M., Neittaanmäki, P., Stenberg, R.: Finite element methods: superconvergence, post-processing and a posteriori estimates. Proc. Conf. Univ. of Jyväskylä, 1996. Lect. Notes Pure Appl. Math., 96.Marcel Dekker New York (1998). MR 1602809; reference:[16] Pehlivanov, A. I., Carey, G. F.: Error estimates for least-squares mixed finite elements.RAIRO, Modélisation Math. Anal. Numér. 28 (1994), 499-516. Zbl 0820.65065, MR 1295584, 10.1051/m2an/1994280504991; reference:[17] Pehlivanov, A. I., Carey, G. F., Lazarov, R. D.: Least-squares mixed finite elements for second order elliptic problems.SIAM J. Numer. Anal. 31 (1994), 1368-1377. Zbl 0806.65108, MR 1293520, 10.1137/0731071; reference:[18] Pehlivanov, A. I., Carey, G. F., Vassilevski, P. S.: Least-squares mixed finite element methods for non-selfadjoint elliptic problems. I: Error estimates.Numer. Math. 72 (1996), 501-522. Zbl 0878.65096, MR 1376110, 10.1007/s002110050179; reference:[19] Raviart, P. A., Thomas, J. M.: A mixed finite element method for 2nd order elliptic problems.Lect. Notes Math. 606 (1977), 292-315. Zbl 0362.65089, MR 0483555, 10.1007/BFb0064470; reference:[20] Wahlbin, L. B.: Superconvergence in Galerkin Finite Element Methods. Lect. Notes Math. 1605.Springer Berlin (1995). MR 1439050

الاتاحة: http://hdl.handle.net/10338.dmlcz/140361

المؤلفون: Brandts, Jan, Korotov, Sergey, Křížek, Michal

مصطلحات موضوعية: keyword:$n$-simplex, keyword:finite element method, keyword:superconvergence, keyword:strengthened Cauchy-Schwarz inequality, keyword:discrete maximum principle, msc:51M20, msc:65N12, msc:65N30

وصف الملف: application/pdf

Relation: mr:MR2316155; zbl:Zbl 1164.65493; reference:[1] B. Achchab, S. Achchab, O. Axelsson, and A. Souissi: Upper bound of the constant in strengthened C.B.S. inequality for systems of linear partial differential equations.Numer. Algorithms 32 (2003), 185–191. MR 1989366, 10.1023/A:1024058625449; reference:[2] B. Achchab, O. Axelsson, A. Laayouni, and A. Souissi: Strengthened Cauchy-Bunyakowski-Schwarz inequality for a three-dimensional elasticity system.Numer. Linear Algebra Appl. 8 (2001), 191–205. MR 1817796, 10.1002/1099-1506(200104/05)8:33.0.CO;2-7; reference:[3] D. N. Arnold, R. Falk, and R. Winther: Finite element exterior calculus.Acta Numer. 15 (2006), 1–135. MR 2269741, 10.1017/S0962492906210018; reference:[4] O. Axelsson: On multigrid methods of the two-level type.In: Multigrid Methods. Lecture Notes in Mathematics, Vol. 960, W. Hackbusch, U. Trotenberg (eds.), Springer-Verlag, Berlin, 1982, pp. 352–367. Zbl 0505.65040, MR 0685778; reference:[5] O. Axelsson, R. 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الاتاحة: http://hdl.handle.net/10338.dmlcz/134674

المؤلفون: Brandts, Jan H.

مصطلحات موضوعية: keyword:superconvergence, keyword:method of lines, keyword:mixed finite elements, keyword:a posteriori error estimation, keyword:adaptive time-stepping, keyword:adaptive refinement, msc:65M15, msc:65M20, msc:65M60

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/134418

المؤلفون: Brandts, Jan H.

مصطلحات موضوعية: keyword:superconvergence, keyword:diffusion equation, keyword:Maxwell equations, keyword:mixed elliptic projection, msc:65M60, msc:65N30, msc:78M10

وصف الملف: application/pdf

Relation: mr:MR1666846; zbl:Zbl 1059.65518; reference:[1] J.H. Brandts: Superconvergence and a posteriori error estimation for triangular mixed finite elements.Num. Math. 68(3) (1994), 311–324. Zbl 0823.65103, MR 1313147, 10.1007/s002110050064; reference:[2] J.H. Brandts: Superconvergence for second order triangular mixed and standard finite elements.Report 9 of: Lab. of Sc. Comp, Univ. of Jyväskylä, Finland, 1996.; reference:[3] J. Douglas and J.E. Roberts: Global estimates for mixed methods for second order elliptic problems.Math. of Comp. 44(169) (1985), 39–52. MR 0771029, 10.1090/S0025-5718-1985-0771029-9; reference:[4] R. Durán: Superconvergence for rectangular mixed finite elements.Num. Math. 58 (1990), 2–15. MR 1075159; reference:[5] P. Monk: A comparison of three mixed methods for the time-dependent Maxwell’s equations.SIAM J. Sci. Stat. Comput. 13(5) (1992), 1097–1122. Zbl 0762.65081, MR 1177800, 10.1137/0913064; reference:[6] P. Monk: An analysis of Nédélec’s method for the spatial discretization of Maxwell’s equations.J. of Comp. Appl. Math. 47 (1993), 101–121. Zbl 0784.65091, MR 1226366, 10.1016/0377-0427(93)90093-Q; reference:[7] P.A. Raviart and J.M. Thomas: A mixed finite element method for second order elliptic problems.Lecture Notes in Mathematics, 606, 1977, pp. 292–315. MR 0483555; reference:[8] : Mathematical theory of finite and boundary element methods.A.H. Schatz, V. Thomeé, and W.L. Wendland (eds.), Birkhäuser Verlag, Basel, 1990. Zbl 0701.00028, MR 1116555

الاتاحة: http://hdl.handle.net/10338.dmlcz/134405

المؤلفون: Zhu, Qiding

مصطلحات موضوعية: keyword:finite element method, keyword:superconvergence error estimates, msc:65N12, msc:65N30

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/134397

المؤلفون: Hlaváček, Ivan, Křížek, Michal, Pištora, Vladislav

مصطلحات موضوعية: keyword:weighted averaged gradient, keyword:linear elements, keyword:nonuniform triangulations, keyword:superapproximation, keyword:superconvergence, msc:65N15, msc:65N30

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/134325

المؤلفون: Hlaváček, Ivan, Chleboun, Jan

مصطلحات موضوعية: keyword:shape optimization, keyword:sensitivity analysis, keyword:superconvergence, keyword:recovered gradient, msc:49D07, msc:65K10, msc:65N30, msc:90C52

وصف الملف: application/pdf

Relation: mr:MR1395687; zbl:Zbl 0870.65050; reference:[1] R.H. Bartels, J. C. Beatty and B.A. Barsky: An Introduction to Splines for use in Computer Graphics and Geometric Modelling.Morgan Kaufmann, Los Altos, 1987. MR 0919732; reference:[2] D. Begis, R. Glowinski: Application de la méthode des éléments finis à l’approximation d’un probléme de domaine optimal.Appl. Math. Optim. 2 (1975), 130–169. MR 0443372, 10.1007/BF01447854; reference:[3] C. de Boor: A Practical Guide to Splines.Springer-Verlag, New York, 1978. Zbl 0406.41003, MR 0507062; reference:[4] V. Braibant, C. Fleury: Aspects theoriques de l’optimisation de forme par variation de noeuds de controle, in Conception optimale de formes (Cours et Séminaires).Tome II, INRIA, Nice, 1983.; reference:[5] J. Chleboun: Hybrid variational formulation of an elliptic state equation applied to an optimal shape problem.Kybernetika 29 (1993), 231–248. Zbl 0805.49024, MR 1231869; reference:[6] J. Chleboun, R.A.E. Mäkinen: Primal hybrid formulation of an elliptic equation in smooth optimal shape problems.Adv. in Math. Sci. and Appl. 5 (1995), 139–162. MR 1325963; reference:[7] P.G. Ciarlet: Basic error estimates for elliptic problems, Handbook of Numerical Analysis II (P.G. Ciarlet, J.L. Lions eds.).North-Holland, Amsterdam, 1991. MR 1115237; reference:[8] J. Haslinger, P. Neittaanmäki: Finite Element Approximation for Optimal Shape Design, Theory and Applications.John Wiley, Chichester, 1988. MR 0982710; reference:[9] E.J. Haug, K.K. Choi and V. Komkov: Design Sensitivity Analysis of Structural Systems.Academic Press, Orlando, London, 1986. MR 0860040; reference:[10] I. Hlaváček: Optimization of the domain in elliptic problems by the dual finite element method.Apl. Mat. 30 (1985), 50–72. MR 0779332; reference:[11] I. Hlaváček, R. Mäkinen: On the numerical solution of axisymmetric domain optimization problems.Appl. Math. 36 (1991), 284–304.; reference:[12] I. Hlaváček, M. Křížek and Pištora: How to recover the gradient of linear elements on nonuniform triangulations.Appl. Math. 41 (1996), 241–267. MR 1395685; reference:[13] I. Hlaváček, M. Křížek: Optimal interior and local error estimates of a recovered gradient of linear elements on nonuniform triangulations.To appear in Journal of Computation. MR 1414854; reference:[14] I. Hlaváček: Shape optimization by means of the penalty method with extrapolation.Appl. Math 39 (1994), 449–477. MR 1298733; reference:[15] J.T. King, S.M. Serbin: Boundary flux estimates for elliptic problems by the perturbed variational method.Computing 16 (1976), 339–347. MR 0418485, 10.1007/BF02252082; reference:[16] M. Křížek, P. Neittaanmäki: On superconvergence techniques.Acta Appl. Math. 9 (1987), 175–198. MR 0900263, 10.1007/BF00047538; reference:[17] R.D. Lazarov, A.I. Pehlivanov, S.S. Chow and G.F. Carey: Superconvergence analysis of the approximate boundary flux calculations.Numer. Math. 63 (1992), 483–501. MR 1189533, 10.1007/BF01385871; reference:[18] R.D. Lazarov, A.I. Pehlivanov: Local superconvergence analysis of the approximate boundary flux calculations.Proceed. of the Conference Equadiff 7, Teubner-Texte zur Math., Bd 118, Leipzig 1990, 275–278.; reference:[19] N. Levine: Superconvergent recovery of the gradient from piecewise linear finite element approximations.IMA J. Numer. Anal. 5 (1985), 407–427. Zbl 0584.65067, MR 0816065, 10.1093/imanum/5.4.407; reference:[20] P.A. Raviart, J.M. Thomas: Primal hybrid finite element method for 2nd order elliptic equations.Math. Comp. 31 (1977), 391–413. MR 0431752; reference:[21] J. Sokolowski, J.P. Zolesio: Introduction to Shape Optimization: Shape Sensitivity Analysis.Springer-Verlag, Berlin, 1992. MR 1215733; reference:[22] L.B. Wahlbin: Superconvergence in Galerkin finite element methods (Lecture notes).Cornell University 1994, 1–243. MR 1439050

الاتاحة: http://hdl.handle.net/10338.dmlcz/134327

المؤلفون: Regińska, Teresa

مصطلحات موضوعية: keyword:superconvergence, keyword:external approximation, keyword:pointwise error estimate, keyword:finite element subspaces, keyword:orthogonal projections, keyword:ordinary differential operators, msc:34B05, msc:65L10

وصف الملف: application/pdf

Relation: mr:MR0949249; zbl:Zbl 0664.65076; reference:[1] J. P. Aubin: Approximation of elliptic boundary value problems.Wiley-Interscience (1972). Zbl 0248.65063, MR 0478662; reference:[2] I. Babuška J. E. Osborn: Generalized finite element methods: their performance and their relation to mixed methods.SIAM J. Numer. Anal. 20 (1983), 510-536. MR 0701094, 10.1137/0720034; reference:[3] C. de Boor B. Swartz: Collocation at Gaussian points.SIAM J. Numer. Anal. 10 (1973), 582-606. MR 0373328, 10.1137/0710052; reference:[4] P. Ciarlet: The finite element method for elliptic problems.North-Holland Publishing Company (1978). Zbl 0383.65058, MR 0520174; reference:[5] C. A. Chandler: Superconvergence for second kind integral equations, Application and Numerical Solution of Integral Equations.Sijthoff, Noordhoff (1980), 103-117. MR 0582986; reference:[6] P. J. Dams: Interpolation and approximation.Blaisdell Publishing Company (1963).; reference:[7] J. Douglas, Jr. T. Dupont: Some superconvergence results for Galerkin methods for the approximate solution of two point boundary problems.Topics in numerical analysis, (1973), 89-92. MR 0366044; reference:[8] J. Douglas, Jr. T. Dupont: Collocation methods for parabolic equations in a single space variable.Lecture Notes in Math. 385 (1974). MR 0483559; reference:[9] T. Dupont: A unified theory of superconvergence for Galerkin methods for two-point boundary value problems.SIAM J. Numer. Anal. vol. 13, no. 3, (1976), 362-368. MR 0408256, 10.1137/0713032; reference:[10] M. Křížek P. Neittaanmäki: On superconvergence techniques.Acta Appl. Math. 9 (1987), 175-198. MR 0900263, 10.1007/BF00047538; reference:[11] T. Regińska: Superconvergence of external approximation for two-point boundary problems.Apl. Mat. 32 (1987), pp. 25-36. MR 0879327; reference:[12] G. R. Richter: Superconvergence of piecewise polynomial Galerkin approximations for Fredholm integral equations of the second kind.Numer. Math. 31 (1978), pp. 63-70. Zbl 0427.65091, MR 0508588, 10.1007/BF01396014; reference:[13] A. Spence K. S. Thomas: On superconvergence properties of Galerkin's method for compact operator equations.IMA J. Numer. Anal. 3 (1983), pp. 253 - 271. MR 0723049, 10.1093/imanum/3.3.253; reference:[14] V. Thomée: Spline approximation and difference schemes for the heat equation. The mathematical foundations of finite element method with application to partial differential equations.Academic Press (1972), pp. 711 - 746. MR 0403265; reference:[15] M. Zlámal: Some superconvergence results in the finite element method.Lecture Notes 606, (1977), p. 353-362. MR 0488863, 10.1007/BFb0064473

الاتاحة: http://hdl.handle.net/10338.dmlcz/104309

المؤلفون: Hlaváček, Ivan, Křížek, Michal

مصطلحات موضوعية: keyword:finite element, keyword:triangular elements, keyword:superconvergence, keyword:post-processing, keyword:averaged gradient, keyword:elliptic systems, msc:35J25, msc:65N15, msc:65N30, msc:73-08, msc:73C99, msc:74S05

وصف الملف: application/pdf

Relation: mr:MR0895878; zbl:Zbl 0636.65115; reference:[1] P. G. Ciarlet: The finite element method for elliptic problems.North-Holland, Amsterdam, New York, Oxford, 1978. Zbl 0383.65058, MR 0520174; reference:[2] I. Hlaváček M. Křížek: On a superconvergent finite element scheme for elliptic systems, I. Dirichlet boundary conditions.Apl. Mat. 32 (1987), 131 -154. MR 0885758; reference:[3] I. Hlaváček J. Nečas: On inequalities of Korn's type.Arch. Rational Mech. Anal. 36 (1970), 305-311, 312-334. 10.1007/BF00249518; reference:[4] M. Křížek P. Neittaanmäki: Superconvergence phenomenon in the finite element method arising from averaging gradients.Numer. Math. 45 (1984), 105-116. MR 0761883, 10.1007/BF01379664; reference:[5] L. A. Oganesjan L. A. Ruchovec: Variational-difference methods for the solution of elliptic equations.Izd. Akad. Nauk Armjanskoi SSR, Jerevan, 1979.; reference:[6] J. Nečas: Les méthodes directes en théorie des équations elliptiques.Academia, Prague, 1967. MR 0227584; reference:[7] M. Zlámal: Some superconvergence results in the finite element method.Mathematical Aspects of Finite Element Methods (Proc. Conf., Rome, 1975). Springer-Verlag, Berlin, Heidelberg, New York, 1977, 353-362. MR 0488863

الاتاحة: http://hdl.handle.net/10338.dmlcz/104251

المؤلفون: Hlaváček, Ivan, Křížek, Michal

مصطلحات موضوعية: keyword:post-processing, keyword:averaged gradient, keyword:Galerkin method, keyword:system, keyword:finite elements, keyword:superconvergence, keyword:global estimate, keyword:elliptic systems, msc:35J25, msc:65N15, msc:65N30, msc:73C99, msc:74S05

وصف الملف: application/pdf

Relation: mr:MR0885758; zbl:Zbl 0622.65097; reference:[1] S. Agmon A. Douglis L. Nirenberg: Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II.Comm. Pure Appl. Math. 17 (1964), 35-92. MR 0162050, 10.1002/cpa.3160170104; reference:[2] A. B. Andreev: Superconvergence of the gradient for linear triangle elements for elliptic and parabolic equations.C. R. Acad. Bulgare Sci. 37 (1984), 293 - 296. Zbl 0575.65106, MR 0758156; reference:[3] I. Babuška A. Miller: The post-processing technique in the finite element method.Parts I-III, Internat. J. Numer. Methods Engrg. 20 (1984), 1085-1109, 1111-1129.; reference:[4] C. M. Chen: Optimal points of the stresses for triangular linear element.Numer. Math. J. Chinese Univ. 2 (1980), 12-20. Zbl 0534.73057, MR 0619174; reference:[5] C. M. Chen: $W^{1,\infty}$-interior estimates for finite element method on regular mesh.J. Comput. Math. 3 (1985), 1-7. Zbl 0603.34024, MR 0815405; reference:[6] P. G. Ciarlet: The finite element method for elliptic problems.North-Holland, Amsterdam, New York, Oxford, 1978. Zbl 0383.65058, MR 0520174; reference:[7] I. Hlaváček M. Hlaváček: On the existence and uniqueness of solutions and some variational principles in linear theories of elasticity with couple-stresses.Apl. Mat. 14 (1969), 387-410. MR 0250537; reference:[8] V. P. Iljin: Svojstva někotorych klassov differenciruemych funkcij mnogich peremennych, zadannych v n-mernoj oblasti.Trudy Mat. Inst. Steklov. 66 (1962), 227-363.; reference:[9] M. Křížek P. Neittaanmäki: Superconvergence phenomenon in the finite element method arising from averaging gradients.Numer. Math. 45 (1984), 105-116. MR 0761883, 10.1007/BF01379664; reference:[10] M. Křížek P. Neittaanmäki: On Superconvergence techniques.Preprint n. 34, Univ. of Jyväskylä, 1984, 1 - 43 (to appear in Acta Appl. Math.). MR 0900263; reference:[11] N. Levine: Superconvergent recovery of the gradient from piecewise linear finite element approximations.IMA J. Numer. Anal. 5 (1985), 407-427. Zbl 0584.65067, MR 0816065, 10.1093/imanum/5.4.407; reference:[12] Q. Lin J. Ch. Xu: Linear finite elements with high accuracy.J. Comput. Math. 3 (1985), 115-133. Zbl 0577.65094, MR 0854355; reference:[13] A. Louis: Acceleration of convergence for finite element solutions of the Poisson equation.Numer. Math. 33 (1979), 43-53. Zbl 0435.65090, MR 0545741, 10.1007/BF01396494; reference:[14] L. A. Oganesjan V. J. Rivkind L. A. Ruchovec: Variational-difference methods for the solution of elliptic equations. Part I.(Proc. Sem., Issue 5, Vilnius, 1973), Inst. of Phys. and Math., Vilnius, 1973, 3-389.; reference:[15] L. A. Oganesjan L. A. Ruchovec: An investigation of the rate of convergence of variational-difference schemes for second order elliptic equations in a two-dimensional regions with smooth boundary.Ž. Vyčisl. Mat. i Mat. Fiz. 9 (1969), 1102-1120. MR 0295599; reference:[16] L. A. Oganesjan L. A. Ruchovec: Variational-difference methods for the solution of elliptic equations.Izd. Akad. Nauk Armjanskoi SSR, Jerevan, 1979.; reference:[17] J. Nečas: Les méthodes directes en théorie des équations elliptiques.Academia, Prague, 1967. MR 0227584; reference:[18] J. Nečas I. Hlaváček: On inequalities of Korn's type.Arch. Rational Mech. Anal. 36 (1970), 305-334. MR 0252844, 10.1007/BF00249518; reference:[19] J. Nečas I. Hlaváček: Mathematical theory of elastic and elasto-plastic bodies: an introduction.Elsevier, Amsterdam, Oxford, New York, 1981. MR 0600655; reference:[20] V. Thomée: High order local approximations to derivatives in the finite element method.Math. Соmр. 31 (1977), 652-660. MR 0438664; reference:[21] B. Westergren: Interior estimates for elliptic systems of difference equations.(Thesis). Univ. of Goteborg, 1982.; reference:[22] Q. D. Zhu: Natural inner Superconvergence for the finite element method.(Proc. China-France Sympos. on the Finite Element method, Beijing, 1982), Science Press, Beijing, Gordon and Breach, New York, 1983, 935-960. MR 0754041; reference:[23] M. Zlámal: Superconvergence and reduced integration in the finite element method.Math. Соmр. 32 (1978), 663-685. MR 0495027

الاتاحة: http://hdl.handle.net/10338.dmlcz/104242

المؤلفون: Regińska, Teresa

مصطلحات موضوعية: keyword:external approximations, keyword:superconvergence, keyword:external method, keyword:Galerkin method, keyword:rate of convergence, keyword:two-point boundary value problems, msc:35B05, msc:65L10

وصف الملف: application/pdf

Relation: mr:MR0879327; zbl:Zbl 0641.65064; reference:[1] J. P. Aubin: Approximation of elliptic boundary-value problems.Wiley-Interscience, New York, 1972. Zbl 0248.65063, MR 0478662; reference:[2] C. De Boor B. Swartz: Collocation at Gausian points.SIAM J. Numer. Anal. 10 (1973), 582-606. MR 0373328, 10.1137/0710052; reference:[3] P. Ciarlet: The finite element method for elliptic problems.North-Holland, Publishing Company (1978). Zbl 0383.65058, MR 0520174; reference:[4] J. Douglas, Jr. T. Dupont: Collocation method for parabolic equations in a single space variable.Lecture Notes in Math., 385 (1974). MR 0483559; reference:[5] J. Douglas, Jr. T. Dupont: Some superconvergence results for Galerkin methods for the approximate solution of two-point boundary problems.- Topics in numerical analysis, ed. J.J.M.F. Miller, pp. 89-92 (1973). MR 0366044; reference:[6] P. J. Davis: Interpolation and approximation.Blaisdell Publishing Company (1963). Zbl 0111.06003, MR 0157156; reference:[7] M. Křížek P. Neittaanmäki: Superconvergence phenomenon in the finite element method arising from averaging gradients.Numer. Math. 45 (1984), pp. 105-116. MR 0761883, 10.1007/BF01379664; reference:[8] T. Regińska: Superconvergence of eigenvalue external approximation for ordinary differential operators.IMA Jour. Numer. Anal. 6 (1986), pp. 309-323. MR 0967671, 10.1093/imanum/6.3.309; reference:[9] M. Zlámal: Some superconvergence results in the finite element method.- Mathematical Aspects of f.e.m., Lecture Notes 606 (1977), pp. 353 - 362. MR 0488863, 10.1007/BFb0064473

الاتاحة: http://hdl.handle.net/10338.dmlcz/104233