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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.

MSC:
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
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[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
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