## Numerical solution of parabolic integro-differential equations by the discontinuous Galerkin method

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- by Stig Larsson, Vidar Thomée and Lars B. Wahlbin PDF
- Math. Comp.
**67**(1998), 45-71 Request permission

## Abstract:

The numerical solution of a parabolic equation with memory is considered. The equation is first discretized in time by means of the discontinuous Galerkin method with piecewise constant or piecewise linear approximating functions. The analysis presented allows variable time steps which, as will be shown, can then efficiently be selected to match singularities in the solution induced by singularities in the kernel of the memory term or by nonsmooth initial data. The combination with finite element discretization in space is also studied.## References

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## Additional Information

**Stig Larsson**- Affiliation: Department of Mathematics, Chalmers University of Technology and Göteborg University, S–412 96 Göteborg, Sweden
- MR Author ID: 245008
- Email: stig@math.chalmers.se
**Vidar Thomée**- Affiliation: Department of Mathematics, Chalmers University of Technology and Göteborg University, S–412 96 Göteborg, Sweden
- MR Author ID: 172250
- Email: thomee@math.chalmers.se
**Lars B. Wahlbin**- Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853
- Email: wahlbin@math.cornell.edu
- Received by editor(s): October 10, 1995
- Received by editor(s) in revised form: August 5, 1996
- Additional Notes: The first two authors were partly supported by the Swedish Research Council for Engineering Sciences (TFR). The third author thanks the National Science Foundation, USA, for financial support and also Chalmers University of Technology and Göteborg University for their hospitality during the Spring of 1995.
- © Copyright 1998 American Mathematical Society
- Journal: Math. Comp.
**67**(1998), 45-71 - MSC (1991): Primary 65M60, 65R20, 45L10
- DOI: https://doi.org/10.1090/S0025-5718-98-00883-7
- MathSciNet review: 1432129