@Article{AAMM-1-201,
author = {Vejchodský , Tomáš and Šolín , Pavel},
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.
Vejchodský , Tomáš and Šolín , Pavel. (2009). 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:
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