Optimal 3D highly anisotropic mesh adaptation based on the continuous mesh framework

Abstract

This paper addresses classical issues that arise when applying anisotropic mesh adaptation to real-life 3D problems as the loss of anisotropy or the necessity to truncate the minimal size when discontinuities are present in the solution. These problematics are due to the complex interaction between the components involved in the adaptive loop: the flow solver, the error estimate and the mesh generator. A solution based on a new continuous mesh framework is proposed to overcome these issues. We show that using this strategy allows an optimal level of anisotropy to be reached and thus enjoy the full benefit of unstructured anisotropic mesh adaptation: optimal distribution of the degrees of freedom, improvement of the ratio accuracy with respect to cpu time,⋯.