An efficient high-order approach to multi-dimensional problems with boundary or interior layers is presented. It combines a coarse grid penaltyspectral element method with a local one-dimensional asymptotic approximation. The solution so obtained is improved by numerical manipulations on the same co
Asymptotic finite element method for boundary value problems
โ Scribed by Pinchas Bar-Yoseph; Moshe Israeli
- Publisher
- John Wiley and Sons
- Year
- 1986
- Tongue
- English
- Weight
- 720 KB
- Volume
- 6
- Category
- Article
- ISSN
- 0271-2091
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โฆ Synopsis
The Asymptotic Finite Element method for improvement of standard finite element solutions of perturbation equations by the addition of asymptotic corrections to the right hand side terms is presented. It is applied here to 1-D and 2-D diffusion-convection equations and to non-linear similarity equations. Excellent results were obtained without the a priori use of special trial and test functions. Theoretical expectations were confirmed.
๐ SIMILAR VOLUMES
We formulate a higher-order (superconvergent) Petrov-Galerkin method by determining, using a finitedifference approximation, the optimal selection of quadratic and cubic modifications to the standard linear test function for bilinear elements. Application of this method to linear elliptic problems r