期刊
SIAM JOURNAL ON SCIENTIFIC COMPUTING
卷 38, 期 3, 页码 A1404-A1429出版社
SIAM PUBLICATIONS
DOI: 10.1137/15M1041109
关键词
enriched Galerkin finite element methods; locally conservative methods; auxiliary space preconditioner; efficient solver; transport equations
资金
- Center for Frontiers of Subsurface Energy Security, an Energy Frontier Research Center - U.S. Department of Energy, Office of Science, and Office of Basic Energy Sciences, under DOE [DE-SC0001114]
- Center for Subsurface Modeling at University of Texas at Austin
- [NSF-DMS 1358953]
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.
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