Study on Error Estimates and Adaptivity: Goal-oriented error estimation and adaptivity in LED discretizations of transport equations

Abstract

A goal-oriented error estimate was derived for LEDdiscretizations of a steady transport equation. The loss of Galerkinorthogonality in the process of flux limiting was shown to provide valuablefeedback for mesh adaptation. The local orthogonality error was employed togenerate an adaptive mesh for circular convection in a 2D domain. Diffusiveterms can be included using gradient recovery to stabilize the residuals andinfer a proper distribution of local errors [197]. Further work willconcentrate on goal-oriented error estimation for unsteady flow problems.