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An error estimate for theH −1 Galerkin method for a parabolic problem with non-smooth initial data

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Abstract

A non-smooth data error estimate with respect to theL 2 norm is shown for a semidiscrete Galerkin-Petrov method for a parabolic problem in one space dimension. If the trial and test spaces consist of piecewise polynomials of degreer−1 inC k anr+1 inC k+2, respectively, with test functions satisfying boundary conditions, then the error norm is bounded byCh r t −r/2 fort positive, whereh is the maximum mesh size.

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References

  1. H. H. Rachford, Jr., M. F. Wheeler,An H −1 Galerkin procedure for the two-point boundary value problem. Mathematical Aspects of Finite Elements in Partial Differential Equations, (1974), C. de Boor, ed., Academic Press, New York, 353–382.

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  2. M. F. Wheeler,An H −1 Galerkin method for parabolic problems in a single space variable, SIAM J. Numer. Anal. 12 (1975), 803–817.

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  3. M. Huang, V. Thomée,Some convergence estimates for semi-discrete type scheme for time-dependent non-selfadjoint parabolic equations. Math. Comp. 37 (1981), 327–346.

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Authors and Affiliations

  1. Dept. of Mathematics, Jilin University, 130023, Changchun, Peoplés Republic of China

    M. Huang

  2. Dept. of Mathematics, Chalmers University of Technology, S-41296, Göteborg, Sweden

    V. Thomée

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  1. M. Huang
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  2. V. Thomée
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Huang, M., Thomée, V. An error estimate for theH −1 Galerkin method for a parabolic problem with non-smooth initial data. Calcolo 19, 115–124 (1982). https://doi.org/10.1007/BF02575682

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  • DOI: https://doi.org/10.1007/BF02575682

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