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Superconvergence of the Galerkin approximation of a quasilinear parabolic equation in a single space variable. (English) Zbl 0435.65094


MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations

Citations:

Zbl 0385.65052
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References:

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[2] J. Douglas, Jr., T. Dupont, L. Wahlbin,Optimal L error estimates for Galerkin approximations to solutions of two-point boundary value problems, Math. Comp.,29, (1975), 475–483. · Zbl 0306.65053
[3] J. Douglas, Jr., T. Dupont, M. F. Wheeler,A quasi-projection analysis of Galerkin methods for parabolic and hyperbolic equations, Math. Comp.,32, (1978), 345–362. · Zbl 0385.65052
[4] A. Friedman,Partial Differential Equations, Holt, Rinehart, Winston, New York, (1969). · Zbl 0224.35002
[5] V. Thomée,Negative norm estimates and superconvergence in Galerkin methods for parabolic problems, preprint no. 1978-6, Department of Mathematics, Chalmers University of Technology, Göteborg.
[6] N. S. Trudinger,On the comparison principle for quasi-linear divergence structure equations, Arch. Rat. Mech. Anal.,57, (1974), 128–133. · Zbl 0311.35046
[7] M. F. Wheeler,A priori L 2 error estimates for Galerkin approximations to paraboblic partial differential equations, SIAM J. Numer. Anal.,10, (1973), 723–759. · Zbl 0258.35041
[8] M. F. Wheeler,L estimates of optimal order for Galerkin methods for one-dimensional second order parabolic and hyperbolic equations, SIAM J. Numer. Anal.,10, (1973), 908–913. · Zbl 0266.65074
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