Abstract
A semilinear second-order singularly perturbed parabolic equation in one space dimension is considered. For this equation, we give computable a posteriori error estimates in the maximum norm for a difference scheme that uses Backward-Euler in time and central differencing in space. Sharp L 1-norm bounds for the Green's function of the parabolic operator and its derivatives are derived that form the basis of the a posteriori error analysis. Numerical results are presented.
Original language | English |
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Pages (from-to) | 189-205 |
Number of pages | 17 |
Journal | Computational Methods in Applied Mathematics |
Volume | 12 |
Issue number | 2 |
DOIs | |
Publication status | Published - Apr 2012 |
Keywords
- A posteriori error estimate
- Backward-Euler
- Maximum norm
- Parabolic equations
- Reaction-diffusion
- Singular perturbation