An approximation of anisotropic metrics from higher order interpolation error for triangular mesh adaptation

Abstract

We propose an efficient algorithm for the numerical approximation of metrics, used for anisotropic mesh adaptation on triangular meshes with finite element computations. We derive the metrics from interpolation error estimates expressed in terms of higher order derivatives, for the Pk-Lagrange finite element, k>1. Numerical examples of mesh adaptation done using metrics computed with our Algorithm, and derived from higher order derivatives as error estimates, show that we obtain the right directions of anisotropy.