Fully space-time metric based anisotropic mesh adaptation for unsteady problems

Abstract

International audienceThis paper presents a novel method for building unstructured meshes for time- dependent problems. We start by introducing the classical anisotropic mesh adaptation technique proposed in [1, 2]. The latter is developed based on the length distribution tensor approach and the associated a posteriori edge based error analysis. Then we extend the mesh adaptation technique to contain adaptive time advancing. A newly developed time error estimator is constructed and intends to homogenize the global error over space and time. The main purpose of this work is the development of a novel meshing algorithm, the paradoxical meshing, that provides optimal space and time meshes suitable for several simulation time subintervals. The advantage of the proposed method relies in its conceptual and computational simplicity as it only requires from the user a number of nodes and a frequency of adaptation according to which the mesh and the time-steps are automatically adapted. Numerical solutions on time-dependent problems demonstrate the accuracy and efficiency of the proposed space-time error estimator