Finite element approximation for degenerate parabolic equations. an application of nonlinear semigroup theory
| Autor: | Akira Mizutani, Norikazu Saito, Takashi Suzuki |
|---|---|
| Rok vydání: | 2005 |
| Předmět: |
Numerical Analysis
Semigroup Applied Mathematics Numerical analysis Mathematical analysis Degenerate energy levels Parabolic partial differential equation Finite element method Computational Mathematics Nonlinear system Rate of convergence Modeling and Simulation Analysis Numerical stability Mathematics |
| Zdroj: | ESAIM: Mathematical Modelling and Numerical Analysis. 39:755-780 |
| ISSN: | 1290-3841 0764-583X |
| DOI: | 10.1051/m2an:2005033 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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