Number of the records: 1
On a Weak Discrete Maximum Principle for hp-FEM
- 1.
SYSNO ASEP 0044977 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Ostatní články Title On a Weak Discrete Maximum Principle for hp-FEM Title Slabý diskrétní princip maxima pro hp-FEM Author(s) Šolín, Pavel (UT-L) RID
Vejchodský, Tomáš (MU-W) RID, SAI, ORCIDSource Title Journal of Computational and Applied Mathematics. - : Elsevier - ISSN 0377-0427
-, č. 209 (2007), s. 54-65Number of pages 11 s. Language eng - English Country NL - Netherlands Keywords discrete maximum principle ; hp-FEM Subject RIV JA - Electronics ; Optoelectronics, Electrical Engineering R&D Projects GA102/05/0629 GA ČR - Czech Science Foundation (CSF) CEZ AV0Z20570509 - UE-C, UT-L (2005-2011) AV0Z10190503 - MU-W (2005-2011) Annotation In this paper we prove a new discrete maximum principle (DMP) for the one-dimensional Poisson equation discretized by the hp-FEM. While the DMP for piecewise-linear elements is a classical result from the 1970s, no extensions to hp-FEM have been available to the present day. Due to a negative result by Hoehn and Mittelmann from 1981, related to quadratic Lagrange elements, it was long assumed that higher-order finite elements do not satisfy discrete maximum principles. In this paper we explain why it is not possible to make a straightforward extension of the classical DMP to the higher-order case, and we propose stronger assumptions on the right-hand side under which an extension is possible. Workplace Institute of Thermomechanics Contact Marie Kajprová, kajprova@it.cas.cz, Tel.: 266 053 154 ; Jana Lahovská, jaja@it.cas.cz, Tel.: 266 053 823 Year of Publishing 2008
Number of the records: 1