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.
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