Domain decomposition by the mortar element method. (English) Zbl 0799.65124

Bernardi, C.; Maday, Y.; Patera, A. T.

Kaper, Hans G. (ed.) et al., Asymptotic and numerical methods for partial differential equations with critical parameters. Proceedings of the NATO Advanced Research Workshop on asymptotic-induced numerical methods for partial differential equations, critical parameters, and domain decomposition, Beaune (France), May 25-28, 1992. Dordrecht: Kluwer Academic Publishers. NATO ASI Ser., Ser. C, Math. Phys. Sci. 384, 269-586 (1993).

Summary: The paper reviews recent results concerning the mortar element method, which allows for coupling variational discretizations of different types on nonoverlapping subdomains. The basic ideas and proofs are recalled on a model problem, and new extensions are presented.
For the entire collection see [Zbl 0772.00030].

MSC:

65N55	Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15	Error bounds for boundary value problems involving PDEs
65N35	Spectral, collocation and related methods for boundary value problems involving PDEs
35J25	Boundary value problems for second-order elliptic equations

Keywords:

domain decomposition; complex geometries; spectral elements; spectral methods; finite elements; error estimate; mortar element method