Discrete Maximum Principle for Poisson Equation with Mixed Boundary Conditions Solved by $hp$-FEM

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

Pavel Solin