Abstract
A singularly perturbed semilinear two-point boundary-value problem is discretized on arbitrary non-uniform meshes. We present second-order maximum norm a posteriori error estimates that hold true uniformly in the small parameter. Their application to monitor-function equidistribution and a posteriori mesh refinement are discussed. Numerical results are presented that support our theoretical estimates.
Original language | English |
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Pages (from-to) | 576-592 |
Number of pages | 17 |
Journal | IMA Journal of Numerical Analysis |
Volume | 27 |
Issue number | 3 |
DOIs | |
Publication status | Published - Jul 2007 |
Keywords
- A posteriori error estimate
- Finite differences
- Grid equidistribution
- Layer-adapted mesh
- Maximum norm
- Reaction-diffusion
- Singular perturbation