@Article{CiCP-3-4,
author = {},
title = {Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems},
journal = {Communications in Computational Physics},
year = {2008},
volume = {3},
number = {4},
pages = {852--877},
abstract = {<p style="text-align: justify;">The maximum principle is a basic qualitative property of the solution of
second-order elliptic boundary value problems. The preservation of the qualitative
characteristics, such as the maximum principle, in discrete model is one of the key
requirements. It is well known that standard linear finite element solution does not
satisfy maximum principle on general triangular meshes in 2D. In this paper we consider how to enforce discrete maximum principle for linear finite element solutions for
the linear second-order self-adjoint elliptic equation. First approach is based on repair
technique, which is a posteriori correction of the discrete solution. Second method
is based on constrained optimization. Numerical tests that include anisotropic cases
demonstrate how our method works for problems for which the standard finite element methods produce numerical solutions that violate the discrete maximum principle.</p>},
issn = {1991-7120},
doi = {https://doi.org/2008-CiCP-7878},
url = {https://global-sci.com/article/81225/enforcing-the-discrete-maximum-principle-for-linear-finite-element-solutions-of-second-order-elliptic-problems}
}