@article{M2AN_2000__34_3_591_0, author = {Ben Belgacem, Faker and Seshaiyer, Padmanabhan and Suri, Manil}, title = {Optimal convergence rates of $hp$ mortar finite element methods for second-order elliptic problems}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique}, volume = {34}, year = {2000}, pages = {591-608}, mrnumber = {1763527}, zbl = {0956.65106}, language = {en}, url = {http://dml.mathdoc.fr/item/M2AN_2000__34_3_591_0} }
Ben Belgacem, Faker; Seshaiyer, Padmanabhan; Suri, Manil. Optimal convergence rates of $hp$ mortar finite element methods for second-order elliptic problems. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 34 (2000) pp. 591-608. http://gdmltest.u-ga.fr/item/M2AN_2000__34_3_591_0/
[1] Méthode itérative de sous-structuration pour les éléments avec joints. C. R. Acad. Sci. Paris Série I 322 (1996) 185-190. | MR 1373759 | Zbl 0836.65118
, and ,[2] Iterative substructuring preconditioners for the mortar finite element method in two dimensions. SIAM. J. Num. Anal. 36 (1999) 551-580. | MR 1675257 | Zbl 0931.65110
, and ,[3] A fast solver for Navier-Stokes equations in the laminar regime using mortar finite element and boundary element methods. SIAM. J. Num. Anal. 32 (1995) 985-1016. | MR 1342280 | Zbl 0833.76032
and ,[4] The h-p-version of the finite element method with quasi-uniform meshes. Modél. Math. et Anal. Numér. 21 (1987) 199-238. | Numdam | MR 896241 | Zbl 0623.65113
and ,[5] The p and h-p-versions of the finite element method: basic principles and properties. SIAM Review 36 (1984) 578-632. | MR 1306924 | Zbl 0813.65118
and ,[6] The optimal convergence rate of the p-Version of the finite element method. SIAM. J. Num. Anal. 24 (1987) 750-776. | MR 899702 | Zbl 0637.65103
and ,[7] Disrétisations 3D non conformes par la méthode de décomposition de domaine des éléments avec joints : Analyse mathématique et mise en oeuvre pour le problème de Poisson. Thèse de l'Université Pierre et Marie Curie, Paris VI. Note technique EDF, ref. HI72/93017 (1993).
,[8] The mortar finite element method with Lagrange multipliers. Num. Mathematik (to appear). | MR 1730018 | Zbl 0944.65114
,[9] Non conforming spectral element methodology tuned to parallel implementation. Compu. Meth. Appl. Mech. Eng. 116 (1994) 59-67. | MR 1286513 | Zbl 0841.65096
and ,[10] Coupling finite element and spectral methods: first results. Math. Compu. 54 (1990),21-39. | MR 995205 | Zbl 0685.65098
, and ,[11] Interpolation of nullspaces for polynomial approximation of divergence-free functions in a cube. Proc. Conf. Boundary Value Problems and Integral Equations in Nonsmooth Domains, M. Costabel, M. Dauge and S. Nicaise Eds., Lecture Notes in Pure and Applied Mathematics 167 Dekker (1994) 27-46. | MR 1301339 | Zbl 0830.46015
, and ,[12] spectral element and mortar element methods. Technical report of the Laboratoire d'analyse numérique, Université Pierre et Marie Curie, Paris VI, 1998. | Zbl 0991.65124
and , Spectral,[13] Relèvement de traces polynomiales et applications. RAIRO Modél. Math. Anal. Numér. 24 (1990)557-611. | Numdam | MR 1076961 | Zbl 0707.65077
and ,[14] A new non conforming approach to domain décomposition: The mortar element method. Pitman, H. Brezis, J.-L. Lions Eds., Collège de France Seminar (1990). | Zbl 0797.65094
, and ,[15] Non conforming matching conditions for coupling spectral and finite element methods. Appl. Numer. Math. 54 (1989) 64-84. | MR 1045019 | Zbl 0684.65099
, and ,[16] Approximate boundary conditions in the finite element method. Symposia Mathematica 10 (1972) 295-313. | MR 403258 | Zbl 0266.73050
, and ,[17] A non-standard finite element interpolation estimate. Research Report 1998:07, Department of Mathematics, University of South Carohna (1998). | Zbl 0938.65133
,[18] The finite element Method for Elliptic Problems. North Holland (1978). | MR 520174 | Zbl 0383.65058
,[19] La méthode des éléments avec joints dans le cas du couplage des méthodes spectrales et méthodes des éléments finis : Résolution des équations de Navier-Stokes. Thèse de l'Université Pierre et Marie Curie, Paris VI (1992).
,[20] On the discretization of inter-domain coupling in elliptic boundary-value problems via the p-Version of the finite element method. T. F. Chan, R. Glowinski, J. Périaux. O.B. Widlund, Eds., SIAM (1989). | MR 992001 | Zbl 0682.65068
,[21] Finite element methods for Navier-Stokes equations. Springer Verlag (1986). | MR 851383 | Zbl 0585.65077
and ,[22] Elliptic problems in nonsmooth domains. Monographs and Studies in Mathematics 24 (Pitman, 1985). | MR 775683 | Zbl 0695.35060
,[23] The h-p-version of the finite element method in one dimension. Num. Mathematik 3 (1986) 577-657. | MR 861522 | Zbl 0614.65088
and ,[24] The h-p-version of the finite element method. Compu. Mech. 1 (1986), Part 1: 21-41, Part 2:203-220. | Zbl 0634.73059
and ,[25] Non-Conjorming h-p finite element methods. Doctoral Thesis, University of Maryland Baltimore County (1998).
,[26] Uniform h-p Convergence results for the mortar finite element method. Math. Compu. PII: S0025-5718(99)01083-2 (to appear). | MR 1649643 | Zbl 0944.65113
and ,[27] Convergence results for the non-Conforming h-p methods. The mortar finite element method. AMS, Cont. Math. 218 (1998) 467-473. | MR 1649643
and ,[28] h-p submeshing via non-conforming finite element methods. Submitted to Compu. Meth. Appl. Mech. Eng. (1998). | Zbl 0971.65101
and ,[29] An analysis of the finite element method. Wellesly, Cambridge Press Masson (1973). | MR 443377 | Zbl 0356.65096
and ,