Discrete Maximum Principle for Poisson Equation with Mixed Boundary Conditions Solved by hp-FEM
Year: 2009
Author: Tomáš Vejchodský, Pavel Solin
Advances in Applied Mathematics and Mechanics, Vol. 1 (2009), Iss. 2 : pp. 201–214
Abstract
We present a proof of the discrete maximum principle (DMP) for the 1D Poisson equation −u″=f equipped with mixed Dirichlet-Neumann boundary conditions. The problem is discretized using finite elements of arbitrary lengths and polynomial degrees (hp-FEM). We show that the DMP holds on all meshes with no limitations to the sizes and polynomial degrees of the elements.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2009-AAMM-10174
Advances in Applied Mathematics and Mechanics, Vol. 1 (2009), Iss. 2 : pp. 201–214
Published online: 2009-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Discrete maximum principle hp-FEM Poisson equation mixed boundary conditions.
Author Details
Tomáš Vejchodský Email
Pavel Solin Email