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Finite element approximation for degenerate parabolic equations. an application of nonlinear semigroup theory

Published online by Cambridge University Press:  15 August 2005

Akira Mizutani ,
Norikazu Saito  and
Takashi Suzuki
Akira Mizutani
Affiliation:
Department of Mathematics, Faculty of Science, Gakushuin University, 1-5-1 Mejiro, Toshima-ku, Tokyo 171-8588, Japan.
Norikazu Saito
Affiliation:
Faculty of Education, Toyama University, 3190 Gofuku, Toyama 930-8555, Japan. saito@edu.toyama-u.ac.jp
Takashi Suzuki
Affiliation:
Division of Mathematical Science, Department of System Innovation, Graduate School of Engineering Science, Osaka University, 1-1 Machikaneyama, Toyonaka, 560-0043, Japan.
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Abstract

Finite element approximation for degenerate parabolic equations is considered. We propose a semidiscrete scheme provided with order-preserving and L1 contraction properties, making use of piecewise linear trial functions and the lumping mass technique. Those properties allow us to apply nonlinear semigroup theory, and the wellposedness and stability in L1 and L∞, respectively, of the scheme are established. Under certain hypotheses on the data, we also derive L1 convergence without any convergence rate. The validity of theoretical results is confirmed by numerical examples.

Keywords

Finite element methoddegenerate parabolic equationnonlinear semigroup.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 39 , Issue 4 , July 2005 , pp. 755 - 780
Copyright
© EDP Sciences, SMAI, 2005

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