H-adaptation for high-order discontinuous Galerkin schemes built on local multiwavelet analysis

Abstract

We develop and analyze error estimators and mesh adaptation strategies within a discontinuous Galerkin formulation. The basic idea of the study is to reduce the computational cost of the simulation by employing mesh adaptation as a better alternative to the use of uniform grids. The novelty of the study resides in the use of multiwavelets and how their remarkable properties may shed new light on driving the adaptation process. This is motivated by the fact that multiwavelets break any input apart into a hierarchy of low resolution data and subsequently finer details. Our error estimator makes use of multiwavelets’ properties while being local to the element, thereby maintaining the parallel efficiency of the solver. Early tests on the one-dimensional viscous Burgers equation have shown convincing results (García Bautista et al. [1]). This work is focused on the laminar backward-facing step configuration to assess the performance of the method in higher dimensions.