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Error estimates for the discontinuous Galerkin methods for parabolic equations. (English) Zbl 1112.65086
The authors develop the error estimates for the discontinuous Galerkin methods for parabolic equations using new assumptions. Several theorems and lemmas are presented for the foundation and finally local optimal approximnations are defined and illstrated. No numerical experiments are performed.

MSC:
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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
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