Discrete Maximum Principle for Poisson Equation with Mixed Boundary Conditions Solved by hp-FEM
Tomas Vejchodsk 1*, Pavel Solin 21 Institute of Mathematics, Czech Academy of Sciences, Zitna 25, CZ-115 67 Praha 1, Czech Republic,
2 Department of Mathematics and Statistics, University of Nevada, Reno, USA, Institute of Thermomechanics, Czech Academy of Sciences, Dolejskova 5, Praha 8, CZ-18200, Czech Republic.
Received 10 December 2008; Accepted (in revised version) 19 January 2009
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.AMS subject classifications: 65N30
Key words: Discrete maximum principle, hp-FEM, Poisson equation, mixed boundary conditions.
Email: email@example.com (T. Vejchodsky), firstname.lastname@example.org (P. Solin)