Optimal error estimates in Jacobi-weighted Sobolev spaces for polynomial approximations on the triangle

@article{Li2010OptimalEE,
  title={Optimal error estimates in Jacobi-weighted Sobolev spaces for polynomial approximations on the triangle},
  author={Huiyuan Li and Jie Shen},
  journal={Math. Comput.},
  year={2010},
  volume={79},
  pages={1621-1646}
}
Spectral approximations on the triangle by orthogonal polynomials are studied in this paper. Optimal error estimates in weighted semi-norms for both the L2− and H1 0−orthogonal polynomial projections are established by using the generalized Koornwinder polynomials and the properties of the Sturm-Liouville operator on the triangle. These results are then applied to derive error estimates for the spectral-Galerkin method for secondand fourthorder equations on the triangle. The generalized… CONTINUE READING