A smooth fictitious domain/multiresolution method for elliptic equations on general domains

Abstract

To cite this version:Ping Yin, Jacques Liandrat. A smooth fictitious domain/multiresolution method for elliptic equations on general domains. AbstractWe propose a smooth fictitious domain/multiresolution method for enhancing the accuracy order in solving second order elliptic partial differential equations on general bivariate domains. We prove the existence and uniqueness of the solution of corresponding discrete problem and the interior error estimate which justifies the improved accuracy order. Numerical experiments are conducted on a cassini oval.