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A Petrov–Galerkin spectral method for fourth‐order problems
Author(s) -
Sun Tao,
Yi Lijun
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2973
Subject(s) - petrov–galerkin method , mathematics , galerkin method , spectral method , order (exchange) , boundary value problem , mathematical analysis , numerical analysis , dirichlet distribution , dirichlet boundary condition , homogeneous , dirichlet problem , finite element method , combinatorics , physics , finance , economics , thermodynamics
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. Copyright © 2013 John Wiley & Sons, Ltd.