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Discrete maximum principle for higher-order finite elements in 1D

Authors: Tomás Vejchodsky and Pavel Solín
Journal: Math. Comp. 76 (2007), 1833-1846
MSC (2000): Primary 65N30; Secondary 35B50
Published electronically: April 30, 2007
MathSciNet review: 2336270
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Abstract: We formulate a sufficient condition on the mesh under which we prove the discrete maximum principle (DMP) for the one-dimensional Poisson equation with Dirichlet boundary conditions discretized by the $ hp$-FEM. The DMP holds if a relative length of every element $ K $ in the mesh is bounded by a value $ H^*_{\rm rel}(p)\in[0.9,1]$, where $ p\ge 1$ is the polynomial degree of the element $ K$. The values $ H^*_{\rm rel}(p)$ are calculated for $ 1 \le p \le 100$.

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Additional Information

Tomás Vejchodsky
Affiliation: Mathematical Institute, Academy of Sciences, Žitná 25, Praha 1, CZ-115 67, Czech Republic

Pavel Solín
Affiliation: Institute of Thermomechanics, Academy of Sciences, Dolejškova 5, Praha 8, CZ-182 00, Czech Republic
Address at time of publication: Department of Mathematical Sciences, University of Texas at El Paso, El Paso, Texas 79968-0514

Keywords: Discrete maximum principle, discrete Green's function, higher-order elements, $hp$-FEM, Poisson equation.
Received by editor(s): January 31, 2006
Received by editor(s) in revised form: July 25, 2006
Published electronically: April 30, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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