FEM-BEM coupling in fractional diffusion

Abstract

We derive and analyze a fully computable discrete scheme for fractional partial differential equations posed on the full space Rᵈ⁠. Based on a reformulation using the well-known Caffarelli–Silvestre extension, we study a modified variational formulation to obtain well-posedness. Our scheme is obtained by combining a diagonalization procedure with a reformulation using boundary integral equations and a coupling of finite elements and boundary elements. For our discrete method we present a-priori estimates as well as numerical examples.