Spectral Method on Quadrilaterals

@inproceedings{BENYU2010SpectralMO,
  title={Spectral Method on Quadrilaterals},
  author={GUO BEN-YU and Jia Hong-Li},
  year={2010}
}
In this paper, we investigate the spectral method on quadrilaterals. We introduce an orthogonal family of functions induced by Legendre polynomials, and establish some results on the corresponding orthogonal approximation. These results play important roles in the spectral method for partial differential equations defined on quadrilaterals. As examples of applications, we provide spectral schemes for two model problems and prove their spectral accuracy in Jacobi weighted Sobolev space… CONTINUE READING