Anisotropic mesh adaptation for high-order finite elements spaces with the log-simplex method. Application to discontinuous Galerkin methods

Abstract

In this article, a high-order solution-based mesh adaptation method is investigated. This later, which is called the log-simplex method, relies on the approximation of high-order differential form of the solution by a dedicated metric-field. The method is a natural extension of Hessian-based methods to the high-order case.