A Petrov-Galerkin spectral method for fourth-order problems

• Published in: Mathematical methods in the applied sciences Vol. 37; no. 15; pp. 2257 - 2270
• Main Authors: Sun, Tao, Yi, Lijun
• Format: Journal Article
• Language: English
• Published: Freiburg Blackwell Publishing Ltd 01.10.2014; Wiley Subscription Services, Inc
• Subjects: Accuracy; Approximation; Boundary conditions; Dirichlet problem; fourth-order problems; Mathematical models; orthogonal approximations; Petrov-Galerkin spectral method; Spectral methods; Two dimensional
• ISSN: 0170-4214; 1099-1476
• DOI: 10.1002/mma.2973

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.