zbMATH — the first resource for mathematics

A multi-domain method for solving numerically multi-scale elliptic problems. (English) Zbl 1049.65145
Summary: We present a family of iterative methods to solve numerically second order elliptic problems with multi-scale data using multiple levels of grids. These methods are based upon the introduction of a Lagrange multiplier to enforce the continuity of the solution and its fluxes across interfaces. This family of methods can be interpreted as a mortar element method with complete overlapping domain decomposition for solving numerically multi-scale elliptic problems.

65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
Full Text: DOI
[1] Belgacem, F.B., The mortar finite element method with Lagrange multipliers, Numer. math., 84, 173-197, (1999) · Zbl 0944.65114
[2] Bernardi, C.; Maday, Y.; Patera, A.T., A new nonconforming approach to domain decomposition: the mortar element method, (), 13-51 · Zbl 0797.65094
[3] Braess, D.; Dahmen, W., The mortar element method revisited – what are the right norms?, (), 27-40 · Zbl 1026.65095
[4] Glowinski, R.; He, J.; Rappaz, J.; Wagner, J., Approximation of multi-scale elliptic problems using patches of finite elements, C. R. acad. sci. Paris, ser. I, 337, 679-684, (2003) · Zbl 1036.65090
[5] R. Glowinski, J. He, J. Rappaz, J. Wagner, A multi-domain method for numerical solution of multi-scale elliptic problems, in preparation · Zbl 1049.65145
[6] Quarteroni, A.; Valli, A., Domain decomposition methods for partial differential equations, (1999), Oxford University Press Oxford · Zbl 0931.65118
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.