A posteriori error estimation for finite-volume solutions of hyperbolic conservation laws Original Research Article

In this paper, an a posteriori error estimation technique for hyperbolic conservation laws is proposed. The error distributions are obtained by solving a system of equations for the errors which are derived from the linearized hyperbolic conservation laws. The error source term is estimated using the modified equation analysis. Numerical tests for one-dimensional linear and non-linear scalar equations and systems of equations are presented. The results demonstrate that the error estimation technique can correctly predict the location and magnitude of the errors. In addition, it is shown in an example that the estimated error source terms can be used for grid adaptation to control the magnitude of error.