Volume 1, Issue 2
Discrete Maximum Principle for Poisson Equation with Mixed Boundary Conditions Solved by hp-FEM

Tomáš Vejchodský and Pavel Šolín

Adv. Appl. Math. Mech., 1 (2009), pp. 201-214.

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  • Abstract

We present a proof of the discrete maximum principle (DMP) for the 1D Poisson equation −u=f equipped with mixed Dirichlet-Neumann boundary conditions. The problem is discretized using finite elements of arbitrary lengths and polynomial degrees (hp-FEM). We show that the DMP holds on all meshes with no limitations to the sizes and polynomial degrees of the elements.

  • History

Published online: 2009-01

  • AMS Subject Headings

65N30

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