We consider the numerical approximation of singularly perturbed elliptic boundary value problems over nonsmooth domains. We use a decomposition of the solution that contains a smooth part, a corner layer part and a boundary layer part. Explicit guidelines for choosing mesh-degree combinations are gi
Finite element superconvergence approximation for one-dimensional singularly perturbed problems
โ Scribed by Zhimin Zhang
- Publisher
- John Wiley and Sons
- Year
- 2002
- Tongue
- English
- Weight
- 481 KB
- Volume
- 18
- Category
- Article
- ISSN
- 0749-159X
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## Abstract The numerical approximation by a lowerโorder anisotropic nonconforming finite element on appropriately graded meshes are considered for solving semisingular perturbation problems. The quasiโoptimalโorder error estimates are proved in the ฮตโweighted __H__^1^โnorm valid uniformly, up to a
A method to construct grid approximations for singularly perturbed boundary value problems for elliptic and parabolic equations, whose solutions contain a parabolic boundary layer, is considered. The grid approximations are based on the fitted operator method. Finite difference schemes, finite eleme