A monotone nonlinear cell-centered finite element method for anisotropic diffusion problems
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Date
2019-11-19
Authors
Dao, Nguyen Anh
Vo, Duc Cam Hai
Ong, Thanh Hai
Journal Title
Journal ISSN
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.
Rights
Attribution 4.0 International