Stability and accuracy of adapted finite element methods for singularly perturbed problems
Copyright policy )Stability and accuracy of adapted finite element methods for singularly perturbed problems
The authors study the stability and accuracy of the standard finite element method (FEM) and a new streamline diffusion finite element method (SDFEM) for the following one-dimensional linear singularly perturbed convection-diffusion two-point boundary-value problems \[ -\varepsilon u'' - b u' = f, \quad (0,1), \quad u(0) = g_0, \quad u(1) = g_1. \] It has been shown that the accuracy of the standard FEM depends crucially on the uniformity of the grid away from the boundary layer. Here, the authors develop a new SDFEM based on a special choice of the stabilization bubble function. The new method is shown to have an optimal maximum norm stability and approximation property. Optimal convergence results for the standard FEM and the new SDFEM are obtained.
- Pennsylvania State University United States
- University of California, Irvine United States
- Peking University China (People's Republic of)
Numerical solution of boundary value problems involving ordinary differential equations, convergence, Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations, streamline diffusion FEM, finite element method, Singular perturbations for ordinary differential equations, equidistribution grid, Linear boundary value problems for ordinary differential equations, stability, Stability and convergence of numerical methods for ordinary differential equations, singular perturbation
Numerical solution of boundary value problems involving ordinary differential equations, convergence, Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations, streamline diffusion FEM, finite element method, Singular perturbations for ordinary differential equations, equidistribution grid, Linear boundary value problems for ordinary differential equations, stability, Stability and convergence of numerical methods for ordinary differential equations, singular perturbation
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