Spectral Galerkin Approximation and Error Estimates Based on Reduced Order Scheme for A Class of Fourth Order Equations
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.
fourth order equationreduced order schemespectral Galerkin approximationerror estimation
万方数据
维普
