Goal-oriented mesh adaptation for finite volume methods using a dissipation-based error indicator
The accuracy of functionals of solutions of the Euler equations, solved using a finite volume code, is examined under grid refinement. It is shown that a commonly used adaptation indicator based on local solution gradients is ineffective in reducing functional error for flows with Supersonic regions. A novel indicator is introduced which attempts to quantify that part of the error in the functional due to the explicitly added dissipation present in the numerical flux. The scheme is considerably simpler and computationally cheaper than other recently proposed a posteriori error estimators for finite volume schemes, but does not account for all sources of error. Note that emphasis is placed on numerical evaluation of the performance of the scheme, and it is shown to be extremely effective in both estimating and reducing error for a wide range of flows. Copyright (C) 2007 John Wiley & Sons, Ltd.
mesh adaptation finite volume a posteriori error estimation sensitivity analysis