一类新的分层基以及非线性Galerkin方法

A New Hierchical Basis and Nonlinear Galerkin Methods

本文首先讨论了一类新的分层基函数，该基函数具有小波和有限元两方面的优点，特别适用于用来构造耗散型发展方程的非线性Ｇａｌｅｒｋｉｎ算法．本文利用该基函数对一类抽象发展方程给出了其非线性Ｇａｌｅｒｋｉｎ算法。并分析了该算法的收敛性，给出了误差估计。

In this paper we first discuss a new kind of hierarchical basis functions whichhave the advantages of both wavelet and finite element,and well adapted to thenonlinear Galerkin methods.Then we apply this basis to the nonlinear Galerkin methods for a class of nonlinear evolution equations,analysis the convergenceof this algorithm,and finaly obtain the error estimates.