Finite element approximation for degenerate parabolic equations. An application of nonlinear semigroup theory
Mizutani, Akira ; Saito, Norikazu ; Suzuki, Takashi
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 39 (2005), p. 755-780 / Harvested from Numdam
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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.

Publié le : 2005-01-01
DOI : https://doi.org/10.1051/m2an:2005033
Classification:  35K65,  47H20,  65M60 
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     author = {Mizutani, Akira and Saito, Norikazu and Suzuki, Takashi},
     title = {Finite element approximation for degenerate parabolic equations. An application of nonlinear semigroup theory},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {39},
     year = {2005},
     pages = {755-780},
     doi = {10.1051/m2an:2005033},
     mrnumber = {2165678},
     zbl = {1078.35009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_2005__39_4_755_0}
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Mizutani, Akira; Saito, Norikazu; Suzuki, Takashi. Finite element approximation for degenerate parabolic equations. An application of nonlinear semigroup theory. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 39 (2005) pp. 755-780. doi : 10.1051/m2an:2005033. http://gdmltest.u-ga.fr/item/M2AN_2005__39_4_755_0/

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