Abstract
A singularly perturbed reaction-diffusion equation is posed in a two-dimensional L-shaped domain Ω subject to a continuous Dirchlet boundary condition. Its solutions are in the Holder space C2/3 (ω̄) and typically exhibit boundary layers and corner singularities. The problem is discretized on a tensor-product Shishkin mesh that is further refined in a neighboorhood of the vertex of angle 37π/2. We establish almost second-order convergence of our numerical method in the discrete maximum norm, uniformly in the small diffusion parameter. Numerical results are presented that support our theoretical error estimate.
Original language | English |
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Pages (from-to) | 2125-2139 |
Number of pages | 15 |
Journal | Mathematics of Computation |
Volume | 77 |
Issue number | 264 |
DOIs | |
Publication status | Published - Oct 2008 |
Keywords
- Corner singularity
- L-shaped domain
- Pointwise error estimate
- Reaction-diffusion
- Second order
- Shishkin mesh
- Singular perturbation