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A Petrov-Galerkin spectral method for fourth-order problems
- Source :
- Mathematical Methods in the Applied Sciences. 37:2257-2270
- Publication Year :
- 2013
- Publisher :
- Wiley, 2013.
-
Abstract
- In this paper, we consider the Petrov–Galerkin spectral method for fourth-order elliptic problems on rectangular domains subject to non-homogeneous Dirichlet boundary conditions. We derive some sharp results on the orthogonal approximations in one and two dimensions, which play important roles in numerical solutions of higher-order problems. By applying these results to a fourth-order problem, we establish the H2-error and L2-error bounds of the Petrov–Galerkin spectral method. Numerical experiments are provided to illustrate the high accuracy of the proposed method and coincide well with the theoretical analysis. Copyright © 2013 John Wiley & Sons, Ltd.
Details
- ISSN :
- 01704214
- Volume :
- 37
- Database :
- OpenAIRE
- Journal :
- Mathematical Methods in the Applied Sciences
- Accession number :
- edsair.doi...........162e1659fc6eabd6dedfee0e253dcdc5