Pointwise error estimates of the bilinear SDFEM on Shishkin meshes
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AbstractA model singularly perturbed convection–diffusion problem in two space dimensions is considered. The problem is solved by a streamline diffusion finite element method (SDFEM) that uses piecewise bilinear finite elements on a Shishkin mesh. We prove that the method is convergent, independently of the diffusion parameter ε, with a pointwise accuracy of almost order 11/8 outside and inside the boundary layers. Numerical experiments support these theoretical results. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013
- Xi’an Jiaotong-Liverpool University China (People's Republic of)
convergence, Error bounds for boundary value problems involving PDEs, convection diffusion problem, Shishkin mesh, 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, Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs, Boundary value problems for second-order elliptic equations, pointwise error estimates, streamline diffusion finite element method, numerical experiments, singular perturbation, Singular perturbations in context of PDEs
convergence, Error bounds for boundary value problems involving PDEs, convection diffusion problem, Shishkin mesh, 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, Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs, Boundary value problems for second-order elliptic equations, pointwise error estimates, streamline diffusion finite element method, numerical experiments, singular perturbation, Singular perturbations in context of PDEs
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