非线性变分问题Galerkin解的收敛性

非线性变分问题Galerkin解的收敛性 THE CONVERGENCE OF GALERKIN SOLUTIONS TO NONLINEAR VARIATIONAL PROBLEMS 雷晋干 Lei Jingan and Zeng Zhonggang first-author 曾钟钢 本文旨在以泛函分析为工具,讨论Hilbert空间中非线性变分边值问题a（u,v）=b（u,v）的Galerkin解的收敛性问题,并在此基础上,讨论了非线性边值问题以及更一般形式的问题的Galerkin解的收敛性。 Some proplems in mathematical physics can be considered as varialional problems such as a（u, v）=b（u, v） with u, v in some Banach spaces. In this paper, we discuss several kinds of variational problems and the convergence and error estimates of their Galerkin solutions by mean of operator theories. As special cases of our conclusions, we effective deal with the nonlinear boundary value problems likeand other somewhat more generalized types of problems based on mathemati cal physics. 1986-04-01 2021-04-01 4