@Article{CiCP-31-5,
author = {Yu, Boyang and Yang, Hongtao and Yonghai, Li and Yuan, Guangwei},
title = {Monotonicity Correction for the Finite Element Method of Anisotropic Diffusion Problems},
journal = {Communications in Computational Physics},
year = {2022},
volume = {31},
number = {5},
pages = {1489--1524},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2021-0197},
url = {https://global-sci.com/article/79554/monotonicity-correction-for-the-finite-element-method-of-anisotropic-diffusion-problems}
}