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中文摘要：
提出一种新的求解Poisson方程的小波有限元方法，采用区间三次Hermite样条小波基作为多尺度有限元插值基函数，并详细讨论了小波有限元提升框架．由于小波基按照给定的内积正交，可实现相应的多尺度嵌套逼近小波有限元求解方程，在不同尺度上的插值基之间完全解耦和部分解耦．数值算例表明在求解Poisson方程时，该方法具有高的效率和精度．
英文摘要：
A new wavelet-based finite element method was proposed for solving Poisson equation. The wavelet bases of Hermite cubic splines on the interval were employed as the multi- scale interpolating basis for finite element analysis. The lifting scheme of wavelet-based finite element method was discussed in details. For the orthogral characteristic of the wavelet bases with respect to the given inner product, the corresponding multi-scale finite element equation will be decoupled across scales totally or partially and be suited for nesting approximation. Some numerical examples indicate that the proposed method has higher efficiency and precision in solving Poisson equation.
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