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Some superconvergence of Galerkin approximations for parabolic and hyperbolic problems in one space dimension. (English) Zbl 0623.65119
Convergence properties of semidiscrete Galerkin methods, using continuous piecewise polynomials, for one space dimension, are studied. It is shown that the approximate solutions and their derivatives have one order better accuracy at certain Jacobi and Gauss points than the optimal order of convergence predicts at arbitrary points. To prove this, elliptic two- point boundary value problems are treated first. Results obtained are used for time dependent problems. Although similar results are known already in literature the importance of the present paper is the fact that the techniques used to prove the results are new and require weaker assumptions.
Reviewer: N.Praagman

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
35L20 Initial-boundary value problems for second-order hyperbolic equations
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
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