Multigrid Methods for Saddle Point Problems: Darcy Systems

preprint2015arXivOpen access

Abstract

We design and analyze multigrid methods for the saddle point problems resulting from Raviart-Thomas-Nédélec mixed finite element methods (of order at least 1) for the Darcy system in porous media flow. Uniform convergence of the WW-cycle algorithm in a nonstandard energy norm is established. Extensions to general second order elliptic problems are also addressed.

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