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
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by Tomáš Vejchodský and Pavel Šolín PDF

Math. Comp. 76 (2007), 1833-1846 Request permission

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 $1 \le p \le 100$.

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