In this paper,we propose a spectral Galerkin approximation and error estimates based on reduced order scheme for a class of fourth order equations.Firstly,by introducing a auxiliary function,we transform the original problems to two coupled second order equa-tions,and their weak form and corresponding discrete format are also derived.Secondly,by using Lax-Milgram lemma and the approxi-mation properties of orthogonal projection operators in non-uniform weighted Sobolev spaces,we strictly prove the existence and uni-queness of weak solution and approximate solution and as well the error estimate.At the end,we conduct some numerical experiments,which show that the algorithm is convergent and high accurate.
关键词
四阶方程/降阶格式/谱Galerkin逼近/误差估计
Key words
fourth order equation/reduced order scheme/spectral Galerkin approximation/error estimation
维普
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