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Optimal Error Estimates and Adaptive Time and Space Step Control for Linear Parabolic Problems

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Numerical Techniques in Continuum Mechanics

Part of the book series: Notes on Numerical Fluid Mechanics ((NNFM,volume 16))

Abstract

In this note we present recent developments in the program for constructing adaptive algorithms for numerical methods for parabolic type problems or stiff initial value prolems that was initiated in Johnson [6] and was continued in Eriksson, Johnson [3] and Johnson, Nie, Thomée [7].

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References

  1. Ciarlet, P., The Finite Element Method for Elliptic Problem, North Holland, Amsterdam (1978).

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  2. Eriksson, K., Johnson, C. and Thomée V., Time discretization of parabolic problems by the Discontinuous Galerkin method, RAIRO, MAN vol. 19 (1985), p. 611–643.

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  3. Eriksson, K. and Johnson, C., Error estimates and automatic time step control for non-linear parabolic problems, I, Preprint no. 1985–20, Department of Mathematics. Chalmers University of Technology, Göteborg, to appear in SIAM J. of Numer. Anal.

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  4. Eriksson, K., Johnson, C. and Lennblad, J., Optimal error estimates and adaptive time and space step control for linear parabolic problems, Preprint no. 1986–06, Department of Mathematics, Chalmers University of Technology, Göteborg.

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  5. Eriksson, K. and Johnson, C., An adaptive finite element method for linear elliptic problems, Preprint no. 1985–13, Department of Mathematics, Chalmers University of Technology, Göteborg.

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  6. Johnson, C. Error estimates and automatic time step control for numerical methods for stiff ordinary differential equations, Preprint no. 1984–27, Department of Mathematics, Chalmers University of Technology, Göteborg, submitted to SIAM J. of Numer. Anal.

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  7. Johnson, C. Nie, Y. and Thomée V., An a posteriori error estimate and automatic time step control for a backward Euler discretization of a parabolic problem, Preprint no. 1985–23, Department of Mathematics, Chalmers University of Technology, Göteborg, submitted to SIAM J. of Numer. Anal.

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Wolfgang Hackbusch Kristian Witsch

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© 1987 Springer Fachmedien Wiesbaden

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Eriksson, K., Johnson, C., Lennblad, J. (1987). Optimal Error Estimates and Adaptive Time and Space Step Control for Linear Parabolic Problems. In: Hackbusch, W., Witsch, K. (eds) Numerical Techniques in Continuum Mechanics. Notes on Numerical Fluid Mechanics, vol 16. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-322-85997-6_1

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  • DOI: https://doi.org/10.1007/978-3-322-85997-6_1

  • Publisher Name: Vieweg+Teubner Verlag, Wiesbaden

  • Print ISBN: 978-3-528-08091-4

  • Online ISBN: 978-3-322-85997-6

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