Abstract
The authors investigate Petrov-Galerkin spectral element method. Some results on Legendre irrational quasi-orthogonal approximations are established, which play important roles in Petrov-Galerkin spectral element method for mixed inhomogeneous boundary value problems of partial differential equations defined on polygons. As examples of applications, spectral element methods for two model problems, with the spectral accuracy in certain Jacobi weighted Sobolev spaces, are proposed. The techniques developed in this paper are also applicable to other higher order methods.
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Dedicated to Professor Roger Temam on the Occasion of his 70th Birthday
Project supported by the National Natural Science Foundation of China (No. 10871131), the Fund for Doctoral Authority of China (No. 200802700001), the Shanghai Leading Academic Discipline Project (No. S30405) and the Fund for E-institutes of Shanghai Universities (No. E03004).
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Jia, H., Guo, B. Petrov-Galerkin spectral element method for mixed inhomogeneous boundary value problems on polygons. Chin. Ann. Math. Ser. B 31, 855–878 (2010). https://doi.org/10.1007/s11401-010-0614-3
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DOI: https://doi.org/10.1007/s11401-010-0614-3
Keywords
- Legendre quasi-orthogonal approximation
- Petrov-Galerkin spectral element method
- Mixed inhomogeneous boundary value problems