Nguyen Anh Dao, Duc Cam Hai Vo, Thanh Hai Ong
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.
Submitted July 3, 2019. Published November 19, 2019.
Math Subject Classifications: 65N08, 65N30, 65N12, 35J15.
Key Words: Discrete maximum principle; heterogeneous anisotropic diffusion;
general grid; finite volume; finite elements; cell-centered scheme.
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| Nguyen Anh Dao Applied Analysis Research Group Faculty of Mathematics and Statistics Ton Duc Thang University Ho Chi Minh City, Vietnam email: daonguyenanh@tdtu.edu.vn | |
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Duc Cam Hai Vo \newline Faculty of Mathematics and Computer Science University of Science, VNU HCMC Ho Chi Minh City, Vietnam email: vdchai@hcmus.edu.vn |
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Thanh Hai Ong Faculty of Mathematics and Computer Science University of Science, VNU HCMC Ho Chi Minh City, Vietnam email: othai@hcmus.edu.vn |
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