Int. J. Numer. Anal. Mod., 6 (2009), pp. 1-16.


Discrete maximum principles for FEM solutions of some nonlinear elliptic interface problems

Janos Karatson 1, Sergey Korotov 2

1 ELTE University, Department of Applied Analysis, H-1518 Budapest, Pf. 120, Hungary.
2 Institute of Mathematics, Helsinki University of Technology, P.O. Box 1100, FI{02015 TKK, Finland.

Received by the editors May 15 2007 and, in revised form, February 12 2008.
Abstract

Discrete maximum principles are proved for finite element discretizations of nonlinear elliptic interface problems with jumps of the normal derivatives. The geometric conditions in the case of simplicial meshes are suitable acuteness or nonobtuseness properties.

AMS subject classifications: 35B50, 35J65, 65N30, 65N50
Key words: Nonlinear elliptic problem, interface problem, maximum principle, discrete maximum principle, finite element method, simplicial mesh.
Email: karatson@cs.elte.hu, sergey.korotov@hut.fi
 

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