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.
BEIRAO DA VEIGA, L., Manzini, G., Putti, M. (2015). Post processing of solution and flux for the nodal mimetic finite difference method. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 31(1), 336-363 [10.1002/num.21907].
Post processing of solution and flux for the nodal mimetic finite difference method
BEIRAO DA VEIGA, LOURENCO;
2015
Abstract
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.
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