Abstract
A singularly perturbed semilinear reaction-diffusion equation, posed in the unit square, is discretized on arbitrary nonuniform tensor-product meshes. We establish a second-order maximum norm a posteriori error estimate that holds true uniformly in the small diffusion parameter. No mesh aspect ratio assumption is made. Numerical results are presented that support our theoretical estimate
| Original language | English |
|---|---|
| Pages (from-to) | 1602-1618 |
| Number of pages | 17 |
| Journal | SIAM Journal on Numerical Analysis |
| Volume | 46 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 11 Apr 2008 |
Keywords
- reaction-diffusion
- singular perturbation
- a posteriori error estimate
- maximum norm
- no mesh aspect ratio condition
- finite differences
- layer-adapted mesh