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

Journal article

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* (p) € [0.9, 1], where p ≥ 1 is the polynomial degree of the element K. The values H* (p) are calculated for 1 ≤ p ≤ 100. © 2007 American Mathematical Society.

Authors: Vejchodský, T; Solín, P

• Journal: Math. Comput.
• Volume: 76
• Issue: 260
• Pages: 1833-1846
• Publication date: 2007-01-01
• DOI: 10.1090/S0025-5718-07-02022-4
• ISSN: 0025-5718