A Petrov–Galerkin spectral method for 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 H2‐error and L2‐error
bounds of the Petrov–Galerkin spectral method. Numerical experiments are provided to …
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 …
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.
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