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

Abstract

Abstract One major hurdle in developing an efficient wavelet‐based numerical method is the difficulty 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 multi‐resolution setting by employing hat interpolation wavelets in the frame of a fictitious 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 effectiveness 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. Copyright © 2003 John Wiley & Sons, Ltd.