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Adv. Appl. Math. Mech., 1 (2009), pp. 201-214. |
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Discrete Maximum Principle for Poisson Equation with Mixed Boundary Conditions Solved by hp-FEM Tomas Vejchodsk 1*, Pavel Solin 2 1 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 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. AMS subject classifications: 65N30Key words: Discrete maximum principle, hp-FEM, Poisson equation, mixed boundary conditions. *Corresponding author. Email: vejchod@math.cas.cz (T. Vejchodsky), solin@utep.edu (P. Solin) |