A Petrov-Galerkin spectral method for fourth-order problems

作者：Sun, Tao; Yi, Lijun^*

来源：Mathematical Methods in the Applied Sciences, 2014, 37(15): 2257-2270.

DOI：10.1002/mma.2973

• Petrov-Galerkin spectral method
• orthogonal approximations
• fourth-order problems

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 H-2-error and L-2-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.

• 出版日期2014-10
• 单位上海师范大学; 上海金融学院