Geodesic
Finite element approximation for degenerate parabolic equations. An application of nonlinear semigroup theory
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 39 (2005) no. 4, pp. 755-780

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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.

DOI : 10.1051/m2an:2005033
Classification : 35K65, 47H20, 65M60
Keywords: finite element method, degenerate parabolic equation, nonlinear semigroup 
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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 },
     pages = {755--780},
     publisher = {EDP-Sciences},
     volume = {39},
     number = {4},
     year = {2005},
     doi = {10.1051/m2an:2005033},
     mrnumber = {2165678},
     zbl = {1078.35009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2005033/}
}
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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 , Tome 39 (2005) no. 4, pp. 755-780. doi: 10.1051/m2an:2005033

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