Multiresolution analysis for finite element method using interpolating wavelet and lifting scheme

Based on interpolating wavelet transform and lifting scheme, a multiresolution analysis for finite element method is developed. By designing appropriate finite element interpolation functions using interpolating wavelet and lifted interpolating wavelet on the interval, the finite element equation may be scale decoupled via eliminating all coupling in the stiffness matrix of element across scales, and then resolved in different spaces independently. The coarse solution can be obtained by solving the equation in the coarse approximation space, and refined by adding details, which can be obtained by solving the equations in the corresponding detail spaces, respectively. The method is well suited to the construction of adaptive algorithm and is powerful in analysing the field problems with changes in gradients and singularities. The numerical examples are given to verify the effectiveness of such a method. Copyright © 2007 John Wiley & Sons, Ltd.