一类基于小波基函数插值的有限元方法

在分析具有大的梯度问题中，将具有紧支集的小波基函数引入到传统的有限元插值函数的构造中，对传统的插值方法进行修正。对新的插值模式进行了数值稳定性（解的唯一存在性）分析并通过分片分析讨论了解的收敛性，新的插值模式所引入的附加自由度通过静力凝聚法来消除，最后得到了基于变分原理的小波有限元列式。

The Finite Element Method Based on Interpolating With Wavelet Basis Function

The compactly supported wavelet basis functions are introduced into the construction of interpolating function of traditional finite element method when analyzing the problems with high gradient, and the traditional interpolating method is modified. The numerical stability of the new interpolating pattern is discussed and the convergence of the new method is also discussed by patch test analysis. The additional freedom of the new interpolating pattern is eliminated by static condensation method. Finally, the wavelet finite element formulations based on variational principles are put forward.