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Some extensions of the local discontinuous Galerkin method for convection-diffusion equations in multidimensions. (English) Zbl 0960.65107
Whiteman, J. R. (ed.), The mathematics of finite elements and applications X, MAFELAP 1999. Proceedings of the 10th conference, Brunel Univ., Uxbridge, Middlesex, GB, June 22-25, 1999. Amsterdam: Elsevier. 225-238 (2000).
Summary: The local discontinuous Galerkin method has been developed recently by B. Cockburn and C.-W. Shu for convection-dominated convection-diffusion equations [SIAM J. Numer. Anal. 35, No. 6, 2440-2463 (1998; Zbl 0927.65118)]. In this paper, we extend the method to multidimensional equations with non-periodic boundary conditions, and with a positive semi-definite diffusion coefficient which may depend on space and time. Stability and a priori error estimates are derived.
For the entire collection see [Zbl 0942.00044].

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K15 Initial value problems for second-order parabolic equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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