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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
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