zbMATH — the first resource for mathematics

The mortar element method for three dimensional finite elements. (English) Zbl 0868.65082
The authors present the application of a new noncomforming domain decomposition approach – the mortar element method – to three-dimensional second-order elliptic problems written under a variational formulation. The case when finite element methods are used in each subdomain is considered. The possibility of dealing with tetrahedra for the finite element grid is shown. An analysis is given of the mortar element method that makes it possible to couple different spectral and finite element methods in adjacent subdomains in a flexible way.

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
Full Text: DOI EuDML
[1] Y. ACHDOU and O. PIRONNEAU, 1995, A fast solver for Navier-Stokes equations in the laminar regime using mortar finite element and boundary element methods SIAM J. Num. Anal., vol. 32,pp. 985-1016. Zbl0833.76032 MR1342280 · Zbl 0833.76032 · doi:10.1137/0732046
[2] G. ANAGNOUSTOU, 1991, Non conforming sliding spectral element methods for the unsteady incompressible Navier-Stokes equations, PhD Thesis, Massachusetts Institute of Technology, Cambridge, Ma. Zbl0724.00029 · Zbl 0724.00029
[3] G. ANAGNOUSTOU, Y. MADAY, C. MAVRIPLIS and A. T. PATERA, 1990, On the mortar element method : generalization and implementation, Proceedings of the third International Conference on Domain Decomposition Methods for P. D. E. eds T. F. Chan, R. Glowinski, J. Pénaux and O. B. Widlund, SIAM, Philadelphia, pp. 157-173. Zbl0704.65077 MR1064342 · Zbl 0704.65077
[4] F. BEN BELGACEM, 1993, Discrétisations 3D nonconformes par la méthode de décomposition de domaines des éléments avec joints : Analyse mathématique et mise en oeuvre pour le problème de Poisson, PhD Thesis, Université Pierre et Marie Curie, Paris, France, Note technique EDF, ref. H172/93017.
[5] F. BEN BELGACEM, 1994, The mortar finite element method with Lagrange multipliers, (Rapport interne MIP, Université Paul Sabatier) (to appear). Zbl0944.65114 MR1730018 · Zbl 0944.65114 · doi:10.1007/s002110050468
[6] F. BEN BELGACEM and Y. MADAY, 1994, Non conforming spectral element methodology tuned to parallel implementation, Comp. Meth. in Applied Mech. Eng, vol. 116, pp. 59-67. Zbl0841.65096 MR1286513 · Zbl 0841.65096 · doi:10.1016/S0045-7825(94)80008-1
[7] F. BEN BELGACEM and Y. MADAY, 1993, Non-conforming spectral method for second order elliptic problems in 3D, Est-West J. of Num. Math., vol. 1-4, pp. 235-252. Zbl0835.65129 MR1318804 · Zbl 0835.65129
[8] C. BERNARDI, N. DEBIT and Y. MADAY, 1990, Coupling spectral and finite element methods for the Laplace equation, Math. Comput., vol. 54-189, pp. 21-41. Zbl0685.65098 MR995205 · Zbl 0685.65098 · doi:10.2307/2008680
[9] C. BERNARDI, Y. MADAY and A. T. PATERA, 1994, A new nonconforming approach to domain decomposition : the mortar element method, Nonlinear Partial Differential Equations and Their Applications, eds H. Brezis and J. L. Lions Pitman, New York, pp. 13-51. Zbl0797.65094 MR1268898 · Zbl 0797.65094
[10] C. BERNARDI, Y. MADAY and A. T. PATERA, 1993, Domain decomposition by the mortar element method, Asymptotic and numerical methods for partial differential equations with critical parameters, eds H. Kaper and M. Garbey, Nato ASI series. Zbl0799.65124 MR1222428 · Zbl 0799.65124
[11] P. E. BJORSTAD and O. B. WIDLUND, 1986, Iterative methods for the solution of elliptic problems in regions partitionned in substructures, SIAM J. Num. Anal., vol. 23, pp. 1097-1120. Zbl0615.65113 MR865945 · Zbl 0615.65113 · doi:10.1137/0723075
[12] N. DÉBIT, 1992, La méthode des éléments avec joints dans le cas du couplage des méthodes spectrales et des éléments finis, PhD Thesis, Université Pierre et Marie Curie, Paris, France.
[13] C. FARHAT and F. X. ROUX, A method of finite element tearing and interconnecting and its parallel solution algorithm, Int. J. Num. Meth. Engr., vol. 32, pp. 1205-1227. Zbl0758.65075 · Zbl 0758.65075 · doi:10.1002/nme.1620320604
[14] P. LE TALLEC and T. SASSI, 1995, ” Domain Decomposition with Nonmatching Grids : Augmented Lagrangian Approach”, Math of Comp., vol. 64, pp. 1367-1396. Zbl0849.65087 MR1308457 · Zbl 0849.65087 · doi:10.2307/2153360
[15] P. LE TALLEC and S. RODRIGUES, 1993, Domain decomposition method with nonmatching grids applied to fluid dynamics, Finite element in fluids, new trends and applications, eds K. Morgan, E. Onate, J. Periaux, J. Peraire and O. C. Zienkiewics, Pineridge Press, Barcelone, pp. 418-426. Zbl0874.76040 MR1292054 · Zbl 0874.76040
[16] C. MAVRIPLIS, 1989, Nonconforming discretization and a posteriori error estimations for adaptive spectral element techniques, PhD Thesis, Massachusetts Institute of Technology, Cambridge, Ma.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.