A posteriori analysis of an IMEX entropy-viscosity formulation for hyperbolic conservation laws with dissipation

摘要

This study considers adjoint based a posteriori estimation of the error in a quantity of interest computed from numerical solutions based on multistage implicit-explicit (IMEX) time integration schemes and an entropy-viscosity formulation for damped hyperbolic partial differential equations (PDEs). Hyperbolic systems are challenging to solve numerically due to the need to stabilize systems with discontinuous or nearly discontinuous solutions in an attempt to limit non-physical oscillations and provide accurate solutions. The goal of this effort is to provide error estimates based on adjoint operators, variational analysis and computable residuals. The error estimates quantify the total error as well as different contributions to the error arising from the time integration schemes and choices of numerical parameters in the numerical method. (C) 2018 IMACS. Published by Elsevier B.V. All rights reserved.