Finite element approximation for degenerate parabolic equations. an application of nonlinear semigroup theory
Department of Mathematics, Faculty of Science,
Gakushuin University, 1-5-1 Mejiro, Toshima-ku, Tokyo 171-8588, Japan.
2 Faculty of Education, Toyama University, 3190 Gofuku, Toyama 930-8555, Japan. email@example.com
3 Division of Mathematical Science, Department of System Innovation, Graduate School of Engineering Science, Osaka University, 1-1 Machikaneyama, Toyonaka, 560-0043, Japan.
Revised: 2 March 2005
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.
Mathematics Subject Classification: 35K65 / 47H20 / 65M60
Key words: Finite element method / degenerate parabolic equation / nonlinear semigroup.
© EDP Sciences, SMAI, 2005