Superconvergence using pointwise interpolation in convection–diffusion problems
Copyright policy )Superconvergence using pointwise interpolation in convection–diffusion problems
Considering a singularly perturbed convection-diffusion problem, we present an analysis for a superconvergence result using pointwise interpolation of Gauß-Lobatto type for higher-order streamline diffusion FEM. We show a useful connection between two different types of interpolation, namely a vertex-edge-cell interpolant and a pointwise interpolant. Moreover, different postprocessing operators are analysed and applied to model problems.
corrected version, 18 pages
- TU Dresden Germany
finite element method, Numerical Analysis (math.NA), 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, layer-adapted meshes, superconvergence, Boundary value problems for second-order elliptic equations, FOS: Mathematics, convection-diffusion problem, Mathematics - Numerical Analysis, singular perturbation, 65N12, 65N30, 65N50, postprocessing, Singular perturbations in context of PDEs
finite element method, Numerical Analysis (math.NA), 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, layer-adapted meshes, superconvergence, Boundary value problems for second-order elliptic equations, FOS: Mathematics, convection-diffusion problem, Mathematics - Numerical Analysis, singular perturbation, 65N12, 65N30, 65N50, postprocessing, Singular perturbations in context of PDEs
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