Abstract
We propose a new multiscale Galerkin method based on interpolation wavelets for two-dimensional Poisson's and plane elasticity problems. The major contributions of the present work are: I) full multiresolution numerical analysis is carried out, 2) general boundaries are handled by a fictitious domain method without using a penalty term or the Lagrange multiplier, 3) no special integration rule is necessary unlike in the (bi-)orthogonal wavelet-based methods, and 4) an efficient adaptive scheme is easy to incorporate. Several benchmark-type problems are considered to show the effectiveness and the potentials of the present approach.
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