Adaptive numerical integration in Element-Free Galerkin methods for elliptic boundary value problems

In this paper we present a new numerical integration scheme for Element-Free Galerkin (EFG) methods used for solving elliptic problems. Integration points are distributed within the problem domain using an adaptive procedure, based on the characteristics of the shape functions. Existing numerical integration schemes for EFG methods do not offer any control over the integration accuracy. We devise a method of distributing the integration points which allows control over the integration accuracy for all elements of the stiffness matrix, while reducing the number of integration points required. The performance of the procedure is demonstrated on test problems in 1D and 2D.