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A locally conservative enriched Galerkin approximation and efficient solver for elliptic and parabolic problems. (English) Zbl 1337.65128

Summary: We present and analyze an enriched Galerkin finite element method (EG) to solve elliptic and parabolic equations with jump coefficients. EG is formulated by enriching the conforming continuous Galerkin finite element method (CG) with piecewise constant functions which can be considered as a penalty stabilization. The method is shown to be locally and globally conservative, while keeping fewer degrees of freedom in comparison with discontinuous Galerkin finite element methods (DG). Moreover, we present and analyze a fast effective EG solver whose cost is roughly that of CG and which can handle an arbitrary order of approximations. A number of numerical tests in two and three dimensions are presented to confirm our theoretical results as well as to demonstrate the advantages of EG when coupled with transport.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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
76M10 Finite element methods applied to problems in fluid mechanics
76S05 Flows in porous media; filtration; seepage

Software:

deal.ii; OpenMPI
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Full Text: DOI

References:

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