Volume 26, Issue 1
A Nonlinear Finite Volume Element Method Satisfying Maximum Principle for Anisotropic Diffusion Problems on Arbitrary Triangular Meshes

Yanni Gao ,  Shuai Wang ,  Guangwei Yuan and Xudeng Hang

10.4208/cicp.OA-2017-0261

Commun. Comput. Phys., 26 (2019), pp. 135-159.

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  • Abstract

A nonlinear finite volume element scheme for anisotropic diffusion problems on general triangular meshes is proposed. Starting with a standard linear conforming finite volume element approximation, a corrective term with respect to the flux jumps across element boundaries is added to make the scheme satisfy the discrete maximum principle. The new scheme is free of the anisotropic non-obtuse angle condition which is a severe restriction on the grids for problems with anisotropic diffusion. Moreover, this manipulation can nearly keep the same accuracy as the original scheme. We prove the existence of the numerical solution for this nonlinear scheme theoretically. Numerical results and a grid convergence study are presented for both continuous and discontinuous anisotropic diffusion problems.

  • History

Published online: 2019-02

  • AMS Subject Headings

65N08, 65N12, 65N15

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