Discrete maximum principle for higher-order finite elements in 1D
Open Access
- 1 October 2007
- journal article
- Published by American Mathematical Society (AMS) in Mathematics of Computation
- Vol. 76 (260), 1833-1847
- https://doi.org/10.1090/s0025-5718-07-02022-4
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 , where is the polynomial degree of the element . The values are calculated for .Keywords
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