A technique to prove parameter-uniform convergence for a singularly perturbed convection-diffusion equation. (English) Zbl 1117.65145
Summary: A priori parameter explicit bounds on the solution of singularly perturbed elliptic problems of convection-diffusion type are established. Regular exponential boundary layers can appear in the solution. These bounds on the solutions and its derivatives are obtained using a suitable decomposition of the solution into regular and layer components. By introducing extensions of the coefficients to a larger domain, artificial compatibility conditions are not imposed in the derivation of these decompositions.
MSC:
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 35B25 | Singular perturbations in context of PDEs |
| 65N15 | Error bounds for boundary value problems involving PDEs |
| 65N06 | Finite difference methods for boundary value problems involving PDEs |
Keywords:
decomposition; regular boundary layers; elliptic equation; singular perturbation; finite differences; convection-diffusion equation; error bounds; convergenceReferences:
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