Volume 1, Issue 2
Discrete Maximum Principle for Poisson Equation with Mixed Boundary Conditions Solved by $hp$-FEM

Adv. Appl. Math. Mech., 1 (2009), pp. 201-214.

Published online: 2009-01

Cited by

Export citation
• 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.

• Keywords

Discrete maximum principle, $hp$-FEM, Poisson equation, mixed boundary conditions.

65N30

• BibTex
• RIS
• TXT
@Article{AAMM-1-201, author = {Tomáš and Vejchodský and and 20613 and and Tomáš Vejchodský and Pavel and Šolín and and 20614 and and Pavel Šolín}, title = {Discrete Maximum Principle for Poisson Equation with Mixed Boundary Conditions Solved by $hp$-FEM}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2009}, volume = {1}, number = {2}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aamm/10174.html} }
TY - JOUR T1 - Discrete Maximum Principle for Poisson Equation with Mixed Boundary Conditions Solved by $hp$-FEM AU - Vejchodský , Tomáš AU - Šolín , Pavel JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 201 EP - 214 PY - 2009 DA - 2009/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/aamm/10174.html KW - Discrete maximum principle, $hp$-FEM, Poisson equation, mixed boundary conditions. AB -

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.

Tomáš Vejchodský & Pavel Šolín. (1970). Discrete Maximum Principle for Poisson Equation with Mixed Boundary Conditions Solved by $hp$-FEM. Advances in Applied Mathematics and Mechanics. 1 (2). 201-214. doi:
Copy to clipboard
The citation has been copied to your clipboard