Numerical Approximation of Second-Order Elliptic Problems in Unbounded Domains

Abstract : This paper deals with the numerical resolution of elliptic problems in unbounded domains using inverted finite elements. In opposition to conventional approaches which are based on the truncation of the domain, the suggested method keeps the domain unbounded and is based on a description of the asymptotic behavior in an appropriate functional framework. The method and its mathematical properties are presented first, and some computational examples are carried out. The obtained numerical results demonstrate the efficiency of the method.