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A discontinuous Galerkin method applied to nonlinear parabolic equations. (English) Zbl 0946.65078
Cockburn, Bernardo (ed.) et al., Discontinuous Galerkin methods. Theory, computation and applications. 1st international symposium on DGM, Newport, RI, USA, May 24-26, 1999. Berlin: Springer. Lect. Notes Comput. Sci. Eng. 11, 231-244 (2000).
Summary: Semidiscrete and a family of discrete time locally conservative discontinuous Galerkin procedures are formulated for approximations to nonlinear parabolic equations. For the continuous time approximations a priori $$L^\infty(L^2)$$ and $$L^2(H^1)$$ estimates are derived and similarly, $$l^\infty(L^2)$$ and $$l^2(H^1)$$ for the discrete time schemes. Spatial rates in $$H^1$$ and time truncation errors in $$L^2$$ are optimal.
For the entire collection see [Zbl 0935.00043].

##### MSC:
 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 65M15 Error bounds for initial value and initial-boundary value problems involving PDEs 35K55 Nonlinear parabolic equations