Year: 2022
Author: Boyang Yu, Hongtao Yang, Yonghai Li, Guangwei Yuan
Communications in Computational Physics, Vol. 31 (2022), Iss. 5 : pp. 1489–1524
Abstract
We apply the monotonicity correction to the finite element method for the anisotropic diffusion problems, including linear and quadratic finite elements on triangular meshes. When formulating the finite element schemes, we need to calculate the integrals on every triangular element, whose results are the linear combination of the two-point pairs. Then we decompose the integral results into the main and remaining parts according to coefficient signs of two-point pairs. We apply the nonlinear correction to the positive remaining parts and move the negative remaining parts to the right side of the finite element equations. Finally, the original stiffness matrix can be transformed into a nonlinear M-matrix, and the corrected schemes have the positivity-preserving property. We also give the monotonicity correction to the time derivative term for the time-dependent problems. Numerical experiments show that the corrected finite element method has monotonicity and maintains the convergence order of the original schemes in $H^1$-norm and $L^2$-norm, respectively.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2021-0197
Communications in Computational Physics, Vol. 31 (2022), Iss. 5 : pp. 1489–1524
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 36
Keywords: The finite element method nonlinear M-matrix monotonicity correction positivity-preserving property two-point pair.
Author Details
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