Interpolation with restrictions in an anisotropic adaptive finite element framework

Abstract

Interpolation operators are important for many applications in scientific computing. During numerical simulations and especially in the context of anisotropic mesh adaptation, with highly stretched elements, the interpolation step is crucial. However, it reduces conservation of important physical quantities and leads to errors that spoil the solution accuracy. In this paper we present a globally conservative method suitable for both interpolations on unstructured fixed and adaptive anisotropic meshes. It consists in combining an a posteriori error estimator that minimizes the interpolation error of the finite element solution followed by an interpolation with restrictions method that conserves physical properties of the field being interpolated. Several numerical examples, in 2D and 3D, are presented and validated to illustrate the efficiency of the approach.