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Superconvergence of mixed finite element methods for parabolic equations. (English) Zbl 0621.65116
The main objective of this paper is the establishment of superconvergence of the solution of a semidiscrete mixed finite element method to the solution of linear parabolic problems in \({\mathbb{R}}^ 2\). A quasi- projection for mixed methods for linear parabolic problems is introduced and then used to produce asymptotic expansions to high order of the mixed method solution. Superconvergence is then derived by post-processing. Optimal order error estimates in Sobolev spaces of negative index are also shown.
Reviewer: N.F.F.Ebecken

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
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