Discrete maximum principle for higher-order finite elements in 1D
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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 $H^*_\textrm {rel}(p)\in [0.9,1]$, where $p\ge 1$ is the polynomial degree of the element $K$. The values $H^*_\textrm {rel}(p)$ are calculated for $1 \le p \le 100$.References
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Additional Information
- Tomáš Vejchodský
- Affiliation: Mathematical Institute, Academy of Sciences, Žitná 25, Praha 1, CZ-115 67, Czech Republic
- Email: vejchod@math.cas.cz
- Pavel Šolín
- 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
- Email: solin@utep.edu
- Received by editor(s): January 31, 2006
- Received by editor(s) in revised form: July 25, 2006
- Published electronically: April 30, 2007
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 76 (2007), 1833-1846
- MSC (2000): Primary 65N30; Secondary 35B50
- DOI: https://doi.org/10.1090/S0025-5718-07-02022-4
- MathSciNet review: 2336270