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 - <p style="text-align: justify;">We present a proof of the discrete maximum principle (DMP) for the
1D Poisson equation $−u&#39;&#39;=f$ 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.</p>