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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 L 1 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 L 1 and L ∞, respectively, of the scheme are established. Under certain hypotheses on the data, we also derive L 1 convergence without any convergence rate.The validity of theoretical results is confirmed by numerical examples.

Keywords

Finite element methoddegenerate parabolic equationnonlinear semigroup.

Information

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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