Construction of a Finite Element Multiresolution Method Based on the Second Generation Wavelets
The second generation wavelet transform has shown the property of high flexibility in multiresolution analysis. Based on this powerful tool, a new finite element multiresolution method is proposed. By using this method, the equation can be resolved in the low-resolution space, and then the coarse solution can be refined by adding the detail solutions in the detail spaces gradually till the solution in a high-resolution space satisfies the expected accuracy. This method is easy to achieve self-adapting algorithm and is suited for solving the singular problems. Numerical tests demonstrate the validity of this method.
Yungang Li, Pengcheng Wang, Liqun Ai, Xiaoming Sang and Jinglong Bu
Y. Lin et al., "Construction of a Finite Element Multiresolution Method Based on the Second Generation Wavelets", Advanced Materials Research, Vols. 291-294, pp. 1161-1164, 2011