المؤلفون: Hannukainen, Antti, Korotov, Sergey, Křížek, Michal

مصطلحات موضوعية: keyword:simplicial element, keyword:maximum angle condition, keyword:interpolation error, keyword:higher-dimensional problem, keyword:$d$-dimensional sine, keyword:semiregular family of simplicial partitions, msc:65N12, msc:65N15, msc:65N30, msc:65N50

وصف الملف: application/pdf

Relation: mr:MR3615475; zbl:Zbl 06738478; reference:[1] Apel, T.: Anisotropic Finite Elements: Local Estimates and Applications.Advances in Numerical Mathematics, Teubner, Stuttgart (1999). Zbl 0934.65121, MR 1716824; reference:[2] Apel, T., Dobrowolski, M.: Anisotropic interpolation with applications to the finite element method.Computing 47 (1992), 277-293. Zbl 0746.65077, MR 1155498, 10.1007/BF02320197; reference:[3] Babuška, I., Aziz, A. K.: On the angle condition in the finite element method.SIAM J. Numer. Anal. 13 (1976), 214-226. Zbl 0324.65046, MR 0455462, 10.1137/0713021; reference:[4] Barnhill, R. E., Gregory, J. A.: Sard kernel theorems on triangular domains with application to finite element error bounds.Numer. Math. 25 (1975), 215-229. Zbl 0304.65076, MR 0458000, 10.1007/BF01399411; reference:[5] Bartoš, P.: The sine theorem for simplexes in $E_n$.Cas. Mat. 93 (1968), 273-277 (In Czech). Zbl 0162.52302, MR 0248604; reference:[6] Brandts, J., Korotov, S., Křížek, M.: On the equivalence of regularity criteria for triangular and tetrahedral finite element partitions.Comput. Math. Appl. 55 (2008), 2227-2233. Zbl 1142.65443, MR 2413688, 10.1016/j.camwa.2007.11.010; reference:[7] Brandts, J., Korotov, S., Křížek, M.: On the equivalence of ball conditions for simplicial finite elements in ${\mathbb R}^d$.Appl. Math. Lett. 22 (2009), 1210-1212. Zbl 1173.52301, MR 2532540, 10.1016/j.aml.2009.01.031; reference:[8] Brandts, J., Korotov, S., Křížek, M.: Generalization of the Zlámal condition for simplicial finite elements in $\mathbb R^d$.Appl. Math., Praha 56 (2011), 417-424. Zbl 1240.65327, MR 2833170, 10.1007/s10492-011-0024-1; reference:[9] Cheng, S.-W., Dey, T. K., Edelsbrunner, H., Facello, M. A., Teng, S.-H.: Sliver exudation.Proc. of the Fifteenth Annual Symposium on Computational Geometry, Miami Beach, 1999 ACM, New York (1999), 1-13. MR 1802189, 10.1145/304893.304894; reference:[10] Ciarlet, P. G.: The Finite Element Method for Elliptic Problems.Studies in Mathematics and Its Applications 4, North-Holland Publishing, Amsterdam (1978). Zbl 0383.65058, MR 0520174; reference:[11] Edelsbrunner, H.: Triangulations and meshes in computational geometry.Acta Numerica (2000), 133-213. Zbl 1004.65024, MR 1883628, 10.1017/s0962492900001331; reference:[12] Eriksson, F.: The law of sines for tetrahedra and $n$-simplices.Geom. Dedicata 7 (1978), 71-80. Zbl 0375.50008, MR 0474009, 10.1007/BF00181352; reference:[13] Hannukainen, A., Korotov, S., Křížek, M.: The maximum angle condition is not necessary for convergence of the finite element method.Numer. Math. 120 (2012), 79-88. Zbl 1255.65196, MR 2885598, 10.1007/s00211-011-0403-2; reference:[14] Jamet, P.: Estimations d'erreur pour des éléments finis droits presque dégénérées.Rev. Franc. Automat. Inform. Rech. Operat. {\it 10}, Analyse numer., R-1 (1976), 43-60. Zbl 0346.65052, MR 0455282; reference:[15] Kobayashi, K., Tsuchiya, T.: A priori error estimates for Lagrange interpolation on triangles.Appl. Math., Praha 60 (2015), 485-499. Zbl 06486922, MR 3396477, 10.1007/s10492-015-0108-4; reference:[16] Kobayashi, K., Tsuchiya, T.: On the circumradius condition for piecewise linear triangular elements.Japan J. Ind. Appl. Math. 32 (2015), 65-76. Zbl 1328.65052, MR 3318902, 10.1007/s13160-014-0161-5; reference:[17] Kobayashi, K., Tsuchiya, T.: Extending Babuška-Aziz's theorem to higher-order Lagrange interpolation.Appl. Math., Praha 61 (2016), 121-133. Zbl 06562150, MR 3470770, 10.1007/s10492-016-0125-y; reference:[18] Křížek, M.: On semiregular families of triangulations and linear interpolation.Appl. Math., Praha 36 (1991), 223-232. Zbl 0728.41003, MR 1109126; reference:[19] Křížek, M.: On the maximum angle condition for linear tetrahedral elements.SIAM J. Numer. Anal. 29 (1992), 513-520. Zbl 0755.41003, MR 1154279, 10.1137/0729031; reference:[20] Kučera, V.: A note on necessary and sufficient conditions for convergence of the finite element method.Proc. Conf. Appl. Math. 2015 (J. Brandts et al., eds.) Institute of Mathematics CAS, Prague (2015), 132-139. Zbl 1363.65189, MR 3700195; reference:[21] Kučera, V.: On necessary and sufficient conditions for finite element convergence.Available at arXiv:1601.02942 (2016). MR 3700195; reference:[22] Kučera, V.: Several notes on the circumradius condition.Appl. Math., Praha 61 (2016), 287-298. Zbl 06587853, MR 3502112, 10.1007/s10492-016-0132-z; reference:[23] Mao, S., Shi, Z.: Error estimates of triangular finite elements under a weak angle condition.J. Comput. Appl. Math. 230 (2009), 329-331. Zbl 1168.65063, MR 2532314, 10.1016/j.cam.2008.11.008; reference:[24] Oswald, P.: Divergence of FEM: Babuška-Aziz triangulations revisited.Appl. Math., Praha 60 (2015), 473-484. Zbl 06486921, MR 3396476, 10.1007/s10492-015-0107-5; reference:[25] Rektorys, K.: Survey of Applicable Mathematics. Vol. I.Mathematics and Its Applications 280, Kluwer Academic Publishers, Dordrecht (1994). Zbl 0805.00002, MR 1282494, 10.1007/978-94-015-8308-4; reference:[26] Strang, G., Fix, G. J.: An Analysis of the Finite Element Method.Prentice-Hall Series in Automatic Computation, Englewood Cliffs, New Jersey (1973). Zbl 356.65096, MR 0443377; reference:[27] Synge, J. L.: The Hypercircle in Mathematical Physics. A Method for the Approximate Solution of Boundary Value Problems.Cambridge University Press, Cambridge (1957). Zbl 0079.13802, MR 0097605; reference:[28] Ženíšek, A.: The convergence of the finite element method for boundary value problems of the system of elliptic equations.Apl. Mat. 14 (1969), 355-377 (In Czech). Zbl 0188.22604, MR 245978; reference:[29] Zlámal, M.: On the finite element method.Numer. Math. 12 (1968), 394-409. Zbl 0176.16001, MR 0243753, 10.1007/BF02161362

الاتاحة: http://hdl.handle.net/10338.dmlcz/145984