期刊
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
卷 31, 期 1, 页码 336-363出版社
WILEY-BLACKWELL
DOI: 10.1002/num.21907
关键词
diffusion problem; mimetic finite difference method; nodal discretization; polygonal and polyhedral mesh; Poisson equation
资金
- National Nuclear Security Administration of the U.S. Department of Energy at Los Alamos National Laboratory [DE-AC52-06NA25396]
- DOE Office of Science Advanced Scientific Computing Research (ASCR) Program in Applied Mathematics
- University of Padua (Progetto Strategico NPDE: Nonlinear partial differential equations, mechanics, and controlled dynamics: analytic, differential geometric, and numerical aspects)
We develop and analyze a post processing technique for the family of low-order mimetic discretizations based on vertex unknowns for the numerical treatment of diffusion problems on unstructured polygonal and polyhedral meshes. The post processing works in two steps. First, from the nodal degrees of freedom, we reconstruct an elemental-based vector field that approximates the gradient of the exact solution. Second, we solve a local problem for each mesh vertex associated with a scheme degree of freedom to determine a post processed normal flux that is conservative and divergence preserving. Theoretical results and numerical experiments for two-dimensional (2D) and 3D benchmark problems show optimal convergence rates. (c) 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 336-363, 2015
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