The sdfem on Shishkin meshes for linear convection-diffusion problems
Copyright policy )The sdfem on Shishkin meshes for linear convection-diffusion problems
The authors consider a modified streamline diffusion finite element method (SDFEM) in order to resolve the boundary layer in some 2D singularly perturbed linear elliptic problems. They use piecewise linear functions on highly nonuniform Shishkin meshes. Moreover, they prove convergence inside the layers, uniformly with respect to the perturbation parameter. Some numerical experiments confirm the theoretical estimations.
- TU Dresden Germany
- National University of Ireland Ireland
convergence, Error bounds for boundary value problems involving PDEs, linear convection-diffusion equation, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Stability and convergence of numerical methods for boundary value problems involving PDEs, modified streamline diffusion finite element method, Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs, Boundary value problems for second-order elliptic equations, error estimates, Shishkin meshes, numerical experiments, singular perturbation, Singular perturbations in context of PDEs
convergence, Error bounds for boundary value problems involving PDEs, linear convection-diffusion equation, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Stability and convergence of numerical methods for boundary value problems involving PDEs, modified streamline diffusion finite element method, Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs, Boundary value problems for second-order elliptic equations, error estimates, Shishkin meshes, numerical experiments, singular perturbation, Singular perturbations in context of PDEs
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