Optimal convergence rates of mortar finite element methods for second-order elliptic problems
Faker Ben Belgacem; Padmanabhan Seshaiyer; Manil Suri
- Volume: 34, Issue: 3, page 591-608
- ISSN: 0764-583X
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topBen Belgacem, Faker, Seshaiyer, Padmanabhan, and 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 34.3 (2000): 591-608. <http://eudml.org/doc/194004>.
@article{BenBelgacem2000,
author = {Ben Belgacem, Faker, Seshaiyer, Padmanabhan, Suri, Manil},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {optimal convergence; mortar finite element methods; second-order elliptic problems; error estimate; non-conforming finite element method; mortar method},
language = {eng},
number = {3},
pages = {591-608},
publisher = {Dunod},
title = {Optimal convergence rates of $hp$ mortar finite element methods for second-order elliptic problems},
url = {http://eudml.org/doc/194004},
volume = {34},
year = {2000},
}
TY - JOUR
AU - Ben Belgacem, Faker
AU - Seshaiyer, Padmanabhan
AU - Suri, Manil
TI - Optimal convergence rates of $hp$ mortar finite element methods for second-order elliptic problems
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2000
PB - Dunod
VL - 34
IS - 3
SP - 591
EP - 608
LA - eng
KW - optimal convergence; mortar finite element methods; second-order elliptic problems; error estimate; non-conforming finite element method; mortar method
UR - http://eudml.org/doc/194004
ER -
References
top- [1] Y. Achdou, Y. Maday and O. B. Widlund, Méthode itérative de sous-structuration pour les éléments avec joints. C. R. Acad. Sci. Paris Série I 322 (1996) 185-190. Zbl0836.65118MR1373759
- [2] Y. Achdou, Y. Maday and O. B. Widlund, Iterative substructuring preconditioners for the mortar finite element method in two dimensions. SIAM. J. Num. Anal. 36 (1999) 551-580. Zbl0931.65110MR1675257
- [3] Y. Achdou and O. Pironneau, 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. Zbl0833.76032MR1342280
- [4] I. Babuška and M. Suri, The h-p-version of the finite element method with quasi-uniform meshes. Modél. Math. et Anal. Numér. 21 (1987) 199-238. Zbl0623.65113MR896241
- [5] I. Babuška and M. Suri, The p and h-p-versions of the finite element method: basic principles and properties. SIAM Review 36 (1984) 578-632. Zbl0813.65118MR1306924
- [6] I. Babuška and M. Suri, The optimal convergence rate of the p-Version of the finite element method. SIAM. J. Num. Anal. 24 (1987) 750-776. Zbl0637.65103MR899702
- [7] F. Ben Belgacem, 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] F. Ben Belgacem, The mortar finite element method with Lagrange multipliers. Num. Mathematik (to appear). Zbl0944.65114MR1730018
- [9] F. Ben Belgacem and Y. Maday, Non conforming spectral element methodology tuned to parallel implementation. Compu. Meth. Appl. Mech. Eng. 116 (1994) 59-67. Zbl0841.65096MR1286513
- [10] C. Bernardi, N. Débit and Y. Maday, Coupling finite element and spectral methods: first results. Math. Compu. 54 (1990),21-39. Zbl0685.65098MR995205
- [11] C. Bernardi, M. Dauge and Y. Maday, 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. Zbl0830.46015MR1301339
- [12] C. Bernardi and Y. Maday, Spectral, spectral element and mortar element methods. Technical report of the Laboratoire d'analyse numérique, Université Pierre et Marie Curie, Paris VI, 1998. Zbl0991.65124
- [13] C. Bernardi and Y. Maday, Relèvement de traces polynomiales et applications. RAIRO Modél. Math. Anal. Numér. 24 (1990)557-611. Zbl0707.65077MR1076961
- [14] C. Bernardi, Y. Maday and A. T. Patera, A new non conforming approach to domain décomposition: The mortar element method. Pitman, H. Brezis, J.-L. Lions Eds., Collège de France Seminar (1990). Zbl0797.65094
- [15] C. Bernardi, Y. Maday and G. Sacchi-Landriam, Non conforming matching conditions for coupling spectral and finite element methods. Appl. Numer. Math. 54 (1989) 64-84. Zbl0684.65099MR1045019
- [16] A. Berger, R. Scott and G. Strang, Approximate boundary conditions in the finite element method. Symposia Mathematica 10 (1972) 295-313. Zbl0266.73050MR403258
- [17] S. Brenner, A non-standard finite element interpolation estimate. Research Report 1998:07, Department of Mathematics, University of South Carohna (1998). Zbl0938.65133
- [18] P.-G. Ciarlet, The finite element Method for Elliptic Problems. North Holland (1978). Zbl0383.65058MR520174
- [19] N. Débit, 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] M. Dorr, 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). Zbl0682.65068MR992001
- [21] V. Girault and P.-A. Raviart, Finite element methods for Navier-Stokes equations. Springer Verlag (1986). Zbl0585.65077MR851383
- [22] P. Grisvard, Elliptic problems in nonsmooth domains. Monographs and Studies in Mathematics 24 (Pitman, 1985). Zbl0695.35060MR775683
- [23] W. Gui and I. Babuška, The h-p-version of the finite element method in one dimension. Num. Mathematik 3 (1986) 577-657. Zbl0614.65088MR861522
- [24] B. Guo and I. Babuška, The h-p-version of the finite element method. Compu. Mech. 1 (1986), Part 1: 21-41, Part 2:203-220. Zbl0634.73059
- [25] P. Seshaiyer, Non-Conjorming h-p finite element methods. Doctoral Thesis, University of Maryland Baltimore County (1998).
- [26] P. Seshaiyer and M. Suri, Uniform h-p Convergence results for the mortar finite element method. Math. Compu. PII: S0025-5718(99)01083-2 (to appear). Zbl0944.65113MR1649643
- [27] P. Seshaiyer and M. Suri, Convergence results for the non-Conforming h-p methods. The mortar finite element method. AMS, Cont. Math. 218 (1998) 467-473. Zbl0909.65075MR1649643
- [28] P. Seshaiyer and M. Suri, h-p submeshing via non-conforming finite element methods. Submitted to Compu. Meth. Appl. Mech. Eng. (1998). Zbl0971.65101
- [29] G. Strang and G. J. Fix, An analysis of the finite element method. Wellesly, Cambridge Press Masson (1973). Zbl0356.65096MR443377
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