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

Vejchodský, Tomáš; Šolín, Pavel

doi:10.1090/S0025-5718-07-02022-4

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
DOI: https://doi.org/10.1090/S0025-5718-07-02022-4
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 -FEM. The DMP holds if a relative length of every element 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 . The values $H^*_{\rm rel}(p)$ are calculated for $1 \le p \le 100$ .

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