A monotone nonlinear cell-centered finite element method for anisotropic diffusion problems

Date

2019-11-19

Authors

Dao, Nguyen Anh
Vo, Duc Cam Hai
Ong, Thanh Hai

Journal Title

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Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

We present a technique to correct the cell-centered finite element scheme [20] (FECC) for full anisotropic diffusion problems on general meshes, which provides a discrete maximum principle (DMP). The correction scheme, named monotone nonlinear cell centered finite element scheme (MNFECC), is cell-centered in the sense that the solution can be computed from cell unknowns of the general primal mesh. Moreover, its coercivity and convergence are proven in a rigorous theoretical framework. Numerical experiments show that the method is effective and accurate, and it satisfies the discrete maximum principle.

Description

Keywords

Discrete maximum principle, Heterogeneous anisotropic diffusion, General grid, Finite volume, Finite elements, Cell-centered scheme

Citation

Dao, N. A., Vo, D. C. H., & Ong, T. H. (2019). A monotone nonlinear cell-centered finite element method for anisotropic diffusion problems. <i>Electronic Journal of Differential Equations, 2019</i>(122), pp. 1-23.

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Attribution 4.0 International

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