Multiscale Galerkin method using interpolation wavelets for two-dimensional elliptic problems in general domains

One major hurdle in developing an e cient wavelet-based numerical method is the di culty in the treatment of general boundaries bounding two- or three-dimensional domains. The objective of this investigation is to develop an adaptive multiscale wavelet-based numerical method which can handle general boundary conditions along curved boundaries. The multiscale analysis is achieved in a multiresolution setting by employing hat interpolation wavelets in the frame of a ctitious domain method. No penalty term or the Lagrange multiplier need to be used in the present formulation. The validity of the proposed method and the e ectiveness of the multiscale adaptive scheme are demonstrated by numerical examples dealing with the Dirichlet and Neumann boundary-value problems in quadrilateral and quarter circular domains