المؤلفون: Vlasák, Miloslav, Lamač, Jan

مصطلحات موضوعية: keyword:a posteriori error estimates, keyword:flux reconstructions, keyword:numerical experiments, msc:65N15, msc:65N30

وصف الملف: application/pdf

الاتاحة: http://hdl.handle.net/10338.dmlcz/703209

المؤلفون: Vejchodský, Tomáš

مصطلحات موضوعية: keyword:a posteriori error estimates, keyword:complementarity, keyword:index of effectivity, keyword:elliptic problem, keyword:reaction-diffusion, keyword:singular perturbation, msc:65N15, msc:65N30

وصف الملف: application/pdf

Relation: zbl:Zbl 06669935

الاتاحة: http://hdl.handle.net/10338.dmlcz/702981

المؤلفون: Vejchodský, Tomáš

مصطلحات موضوعية: keyword:Friedrichs' constant, keyword:a posteriori error estimates, keyword:eigenvalue problem, msc:65N08, msc:65N25, msc:65N30

وصف الملف: application/pdf

الاتاحة: http://hdl.handle.net/10338.dmlcz/702727

المؤلفون: Zhang, Tie, Zhang, Shuhua, Azari, Hossein

مصطلحات موضوعية: keyword:finite element approximation, keyword:a priori error estimates, keyword:a posteriori error estimates, keyword:numerical examples, keyword:variational inequality, keyword:stability, msc:49J40, msc:49M25, msc:65K15, msc:65N12, msc:65N15, msc:65N30

وصف الملف: application/pdf

Relation: mr:MR3204423; zbl:Zbl 1313.65176

الاتاحة: http://hdl.handle.net/10338.dmlcz/702917

المؤلفون: Vejchodský, Tomáš

مصطلحات موضوعية: keyword:second-order boundary value problems, keyword:a posteriori error estimates, keyword:complementary energy, keyword:Friedrichs’ inequality, keyword:numerical example, msc:35A23, msc:35J25, msc:65N15, msc:65N30

وصف الملف: application/pdf

Relation: mr:MR3204419; zbl:Zbl 1313.65296

الاتاحة: http://hdl.handle.net/10338.dmlcz/702913

المؤلفون: Segeth, Karel

مصطلحات موضوعية: keyword:a posteriori error estimates, keyword:finite element method, keyword:biharmonic problem, msc:35J40, msc:65N15, msc:65N30

وصف الملف: application/pdf

الاتاحة: http://hdl.handle.net/10338.dmlcz/702755

المؤلفون: Vejchodský, Tomáš

مصطلحات موضوعية: keyword:complementarity, keyword:guaranteed upper error bounds, keyword:method of hypercircle, keyword:a posteriori error estimates, keyword:error majorants, msc:65N15, msc:65N30

وصف الملف: application/pdf

الاتاحة: http://hdl.handle.net/10338.dmlcz/702760

المؤلفون: Šebestová, Ivana, Dolejší, Vít

مصطلحات موضوعية: keyword:a posteriori error estimates, keyword:discontinuous Galerkin, keyword:heat equation, msc:65M15, msc:65M60

وصف الملف: application/pdf

الاتاحة: http://hdl.handle.net/10338.dmlcz/702754

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

Relation: mr:MR2530543; zbl:Zbl 1212.65256; reference:[1] Alt, W.: On the approximation of infinite optimisation problems with an application to optimal control problems.Appl. Math. Optimization 12 (1984), 15-27. MR 0756510, 10.1007/BF01449031; reference:[2] Atkinson, K. E.: The Numerical Solution of Integral Equations of the Second Kind.Cambridge University Press Cambridge (1997). Zbl 0899.65077, MR 1464941; reference:[3] Babuška, I., A. K. Aziz \rm(eds.): The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations.Academic Press New York (1972). MR 0347104; reference:[4] Becker, R., Kapp, H., Rannacher, R.: Adaptive finite element methods for optimal control of partial differential equations: Basic concept.SIAM J. Control Optim. 39 (2000), 113-132. 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الاتاحة: http://hdl.handle.net/10338.dmlcz/140364

المؤلفون: Jia, Shanghui, Xie, Hehu, Yin, Xiaobo, Gao, Shaoqin

مصطلحات موضوعية: keyword:Stokes eigenvalue problem, keyword:stream function-vorticity-pressure method, keyword:asymptotic expansion, keyword:extrapolation, keyword:a posteriori error estimates, keyword:nonconforming finite element methods, keyword:convergence, msc:35A35, msc:35P05, msc:35P15, msc:35Q30, msc:35Q35, msc:65N12, msc:65N15, msc:65N25, msc:65N30, msc:76D07, msc:76M10

وصف الملف: application/pdf

Relation: mr:MR2476018; zbl:Zbl 1212.65434; reference:[1] Babuška, I., Osborn, J. F.: Estimate for the errors in eigenvalue and eigenvector approximation by Galerkin methods with particular attention to the case of multiple eigenvalue.SIAM J. Numer. Anal. 24 (1987), 1249-1276. MR 0917451, 10.1137/0724082; reference:[2] Babuška, I., Osborn, J. F.: Finite element-Galerkin approximation of the eigenvalues and eigenvectors of selfadjoint problems.Math. Comput. 52 (1989), 275-297. MR 0962210, 10.1090/S0025-5718-1989-0962210-8; reference:[3] Bercovier, M., Pironneau, O.: Error estimates for finite element method solution of the Stokes problem in the primitive variables.Numer. Math. 33 (1979), 211-224. Zbl 0423.65058, MR 0549450, 10.1007/BF01399555; reference:[4] Brezzi, F., Fortin, M.: Mixed and Hybrid Finite Element Methods. Springer Series in Computational Mathematics Vol. 15.Springer New York (1991). 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الاتاحة: http://hdl.handle.net/10338.dmlcz/140344

المؤلفون: Chen, Wei, Lin, Qun

مصطلحات موضوعية: keyword:eigenvalue problem, keyword:Stokes problem, keyword:stream function-vorticity-pressure method, keyword:asymptotic expansion, keyword:extrapolation, keyword:a posteriori error estimates, msc:35Q30, msc:65N25, msc:65N30, msc:76D07

وصف الملف: application/pdf

Relation: mr:MR2197324; zbl:Zbl 1164.65489; reference:[1] I. Babuška, J. Osborn: Eigenvalue problems.Handbook of Numerical Analysis, Vol. II, Finite Element Method (Part I), P. G. Ciarlet, J. L. Lions (eds.), North-Holland Publ., Amsterdam, 1991, pp. 641–787. MR 1115240; reference:[2] M. Bercovier, O. Pironneau: Error estimates for finite element method solution of the Stokes problem in the primitive variables.Numer. Math. 33 (1979), 211–224. MR 0549450, 10.1007/BF01399555; reference:[3] P. E. Bjørstad, B. P. Tjøstheim: High precision solutions of two fourth order eigenvalue problems.Computing 63 (1999), 97–107. MR 1736662, 10.1007/s006070050053; reference:[4] D. Boffi, F. Brezzi, and L. Gastaldi: On the problem of spurious eigenvalues in the approximation of linear elliptic problems in mixed form.Math. Comput. 69 (2000), 121–140. MR 1642801, 10.1090/S0025-5718-99-01072-8; reference:[5] D. Boffi, F. Brezzi, and L. Gastaldi: On the convergence of eigenvalues for mixed formulations.Ann. 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الاتاحة: http://hdl.handle.net/10338.dmlcz/134631

المؤلفون: Vejchodský, Tomáš

مصطلحات موضوعية: keyword:a posteriori error estimates, keyword:finite elements, keyword:nonlinear parabolic problems, keyword:effectivity index, keyword:singly implicit Runge-Kutta methods (SIRK), msc:65L06, msc:65M15, msc:65M20, msc:65M60

وصف الملف: application/pdf

Relation: mr:MR1966345; zbl:Zbl 1099.65091; reference:[1] A. Adjerid, J. E. Flaherty and Y. J. Wang: A posteriori error estimation with finite element methods of lines for one-dimensional parabolic systems.Numer. Math. 65 (1993), 1–21. MR 1217436, 10.1007/BF01385737; reference:[2] J. C. Butcher: A transformed implicit Runge-Kutta method.J. Assoc. Comput. Mach. 26 (1979), 731–738. Zbl 0439.65057, MR 0545546, 10.1145/322154.322163; reference:[3] K. Burrage: A special family of Runge-Kutta methods for solving stiff differential equations.BIT 18 (1978), 22–41. Zbl 0384.65034, MR 0483458, 10.1007/BF01947741; reference:[4] P. G. Ciarlet: The Finite Element Method for Elliptic Problems.North-Holland Publishing Company, Amsterdam, New York, Oxford, 1978. Zbl 0383.65058, MR 0520174; reference:[5] S. Fučík, A. Kufner: Nonlinear Differential Equations.Elsevier Scientific Publishing Company, Amsterdam, Oxford, New York, 1980. MR 0558764; reference:[6] H. Gajevski, K. Gröger and K. Zacharias: Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen.Akademie-Verlag, Berlin, 1974. MR 0636412; reference:[7] I. Hlaváček, M. Křížek and J. Malý: On Galerkin approximations of a quasilinear nonpotential elliptic problem of a nonmonotone type.J. Math. Anal. Appl. 184 (1994), 168–189. MR 1275952, 10.1006/jmaa.1994.1192; reference:[8] S. Larsson, V. Thomée and N. Y. Zhang: Interpolation of coefficients and transformation of the dependent variable in the finite element methods for the nonlinear heat equation.Math. Methods Appl. Sci. 11 (1989), 105–124. MR 0973559, 10.1002/mma.1670110108; reference:[9] P. K. Moore: A posteriori error estimation with finite element semi- and fully discrete methods for nonlinear parabolic equations in one space dimension.SIAM J. Numer. Anal. 31 (1994), 149–169. Zbl 0798.65089, MR 1259970, 10.1137/0731008; reference:[10] P. K. Moore, J. E. Flaherty: High-order adaptive solution of parabolic equations I. Singly implicit Runge-Kutta methods and error estimation.Rensselaer Polytechnic Institute Report 91-12, Troy, NY, Department of Computer Science, Rensselaer Polytechnic Institute, 1991.; reference:[11] P. K. Moore, J. E. Flaherty: High-order adaptive finite element-singly implicit Runge-Kutta methods for parabolic differential equations.BIT 33 (1993), 309–331. MR 1326022, 10.1007/BF01989753; reference:[12] T. Roubíček: Nonlinear differential equations and inequalities.Mathematical Institute of Charles University, Prague, in preparation.; reference:[13] K. Segeth: A posteriori error estimation with the finite element method of lines for a nonlinear parabolic equation in one space dimension.Numer. Math. 33 (1999), 455–475. Zbl 0936.65113, MR 1715561, 10.1007/s002110050459; reference:[14] B. Szabó, I. Babuška: Finite Element Analysis.John Wiley & Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore, 1991. MR 1164869; reference:[15] V. Thomée: Galerkin Finite Element Methods for Parabolic Problems.Springer, Berlin, 1997. MR 1479170

الاتاحة: http://hdl.handle.net/10338.dmlcz/134523

المؤلفون: Tran, Van Bon

مصطلحات موضوعية: keyword:semi-coercive elliptic problems, keyword:Poisson equation, keyword:finite elements, keyword:convergence, keyword:dual problem, keyword:a posteriori error estimates, keyword:variational inequalities, msc:35J05, msc:65N15, msc:65N30

وصف الملف: application/pdf

Relation: mr:MR0934370; zbl:Zbl 0638.65077; reference:[1] I. Hlaváček: Dual finite element analysis for semi-coercive unilateral boundary value problems.Apl. Mat. 23 (1978), 52-71. MR 0480160; reference:[2] I. Hlaváček: Dual finite element analysis for elliptic problems with obstacles on the boundary.Apl. Mat. 22 (1977), 244-255. MR 0440958; reference:[3] J. Haslinger I. Hlaváček: Convergence of a finite element method based on the dual variational formulation.Apl. Mat. 21 (1976), 43-65. MR 0398126; reference:[4] R. S. Falk: Error estimate for the approximation of a class of variational inequalities.Math. Comp. 28 (1974), 963-971. MR 0391502, 10.1090/S0025-5718-1974-0391502-8; reference:[5] F. Brezzi W. W. Hager P. A. Raviart: Error estimates for the finite element solution of variational inequalities. Part I: Primal Theory.Numer. Math. 28 (1977), 431-443. MR 0448949, 10.1007/BF01404345; reference:[6] J. Haslinger: Finite element analysis for unilateral problem with obstacles on the boundary.Apl. Mat. 22 (1977), 180-188. MR 0440956; reference:[7] I. Hlaváček: Dual finite element analysis for unilateral boundary value problems.Apl. Mat. 22 (1977), 14-51. MR 0426453; reference:[8] I. Hlaváček: Convergence of dual finite element approximations for unilateral boundary value problems.Apl. Mat. 25 (1980), 375-386. MR 0590491; reference:[9] J. Céa: Optimisation, théorie et algorithmes.Dunod, Paris 1971. MR 0298892

الاتاحة: http://hdl.handle.net/10338.dmlcz/104282

المؤلفون: Hlaváček, Ivan

مصطلحات موضوعية: keyword:elliptic model problem, keyword:dual variational formulation, keyword:piecewise linear finite elements, keyword:a priori error estimates, keyword:a posteriori error estimates, keyword:two-sided bounds, msc:35J25, msc:65K10, msc:65N15, msc:65N30

وصف الملف: application/pdf

Relation: mr:MR0440958; zbl:Zbl 0422.65065; reference:[1] J. Nečas: Les méthodes directes en théorie des équations elliptiques.Academia, Prague 1967. MR 0227584; reference:[2] G. N. Jakovlev: Boundary properties of functions of class $W_p^{(1)}$ on the domains with angular points.(in Russian). DAN SSSR, 140 (1961), 73-76. MR 0136988; reference:[3] I. Hlaváček: Dual finite element analysis for unilateral boundary value problems.Aplikace matematiky 22 (1977), 14-51. MR 0426453; reference:[4] J. Céa: Optimisation, théorie et algorithmes.Dunod, Paris 1971. MR 0298892; reference:[5] U. Mosco G. Strang: One-sided approximations and variational inequalities.Bull. Am. Soc. 80 (1974), 308-312. MR 0331818, 10.1090/S0002-9904-1974-13477-4; reference:[6] I. Hlaváček: Some equilibrium and mixed models in the finite element method.Proceedings of the Banach Internat. Math. Center, Warsaw (to appear). MR 0514379

الاتاحة: http://hdl.handle.net/10338.dmlcz/103701

المؤلفون: Hlaváček, Ivan

مصطلحات موضوعية: keyword:dual approach, keyword:bilateral boundary value problems, keyword:elliptic equations, keyword:Signorini’s type, keyword:model problems, keyword:asymptotic order of convergence, keyword:finite element approximation, keyword:numerical solution, keyword:a posteriori error estimates, keyword:two-sided estimates, msc:35J25, msc:65N15, msc:65N30

وصف الملف: application/pdf

Relation: mr:MR0426453; zbl:Zbl 0416.65070; reference:[1] J. P. Aubin H. G. Burchard: Some aspects of the method of the hypercircle applied to elliptic variational problems.Num. sol. PDE-II, SYNSPADE (1970), 1-67. MR 0285136; reference:[2] I. Hlaváček: Some equilibrium and mixed models in the finite element method.Proceedings of the St. Banach Internat. Math. Center, Warsaw, (1976).; reference:[3] J. Haslinger I. Hlaváček: Convergence of a finite element method based on the dual variational formulation.Apl. mat. 21 (1976), 43 - 65. MR 0398126; reference:[4] G. Fichera: Boundary value problems of elasticity with unilateral constraints.Encyclopedia of Physics, ed. S. Flügge, Vol. VIa/2, Springer, Berlin 1972.; reference:[5] J. Céa: Optimisation, théorie et algorithmes.Dunod, Paris 1971. MR 0298892; reference:[6] J. Nečas: Les méthodes directes en théorie des équations elliptiques.Academia, Prague 1967. MR 0227584; reference:[7] U. Mosco G. Strang: One-sided approximations and variational inequalities.Bull. Am. Math. Soc. 80 (1974), 308-312. MR 0331818, 10.1090/S0002-9904-1974-13477-4; reference:[8] J. H. Bramble M. Zlámal: Triangular elements in the finite element method.Math. Соmр. 24 (1970), 809-820. MR 0282540; reference:[9] G. Zoutendijk: Methods of feasible directions.Elsevier, Amsterdam 1960. Zbl 0097.35408; reference:[10] I. Hlaváček: Dual finite element analysis for elliptic problems with obstacles on the boundary.Apl. mat. 22 (to appear).

الاتاحة: http://hdl.handle.net/10338.dmlcz/103675