On Error Estimation and Grid Adaptation for Hyperbolic Conservation Laws

摘要

In this paper, the relation between discretisation error, solution error and grid adaptation for hyperbolic conservation laws is investigated. First, it will be presented briefly how error estimators can be obtained by solving a system of equations for the errors which are derived from the linearized hyperbolic conservation laws. Second, it will be shown that grid adaptation can be achieved based on the error source distribution. This technique accounts for convection of errors. Numerical tests for one-dimensional Euler equations are presented. The results show that grid adaptation using the error source distribution could be more efficient than adapting based on the solution error itself. This illustrates the non-local nature of the error and its estimation process for hyperbolic conservation laws.