A Uniformly Convergent Galerkin Method on a Shishkin Mesh for a Convection-Diffusion Problem
Copyright policy )A Uniformly Convergent Galerkin Method on a Shishkin Mesh for a Convection-Diffusion Problem
Two results on convergence uniform in the singular perturbation parameter are given for a singularly perturbed linear elliptic boundary value problem in two dimensions. Their error bounds are of order (i) \((\ln N/N)\) in a global energy norm and (ii) \((\ln N)^{3/2}/\sqrt N\) pointwise near the outflow boundary.
- Dublin City University Ireland
- University College Cork Ireland
convergence, Error bounds for boundary value problems involving PDEs, Applied Mathematics, Shishkin mesh, error bounds, Stability and convergence of numerical methods for boundary value problems involving PDEs, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs, Boundary value problems for second-order elliptic equations, convection-diffusion problem, singular perturbation, Analysis, Singular perturbations in context of PDEs
convergence, Error bounds for boundary value problems involving PDEs, Applied Mathematics, Shishkin mesh, error bounds, Stability and convergence of numerical methods for boundary value problems involving PDEs, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs, Boundary value problems for second-order elliptic equations, convection-diffusion problem, singular perturbation, Analysis, Singular perturbations in context of PDEs
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