Error estimation using the error transport equation for finite-volume methods and arbitrary meshes

摘要

We present a single grid error estimation technique based on the derivation of a continuous equation for the discretization error It is developed in the context of finite-volume methods for arbitrary meshes. The key issue of the evaluation of the source term is addressed through the use of a reconstruction operator. Using a higher order accurate evaluation of this term and solving the error equation with the same numerical methods and on the same computational grid as the primal problem leads to a higher order accurate error prediction. The methodology is presented in detail and its properties of asymptotic exactness and superconvergence are illustrated on several cases, including an application of practical engineering complexity. Also presented is the derivation of a powerful criterium for driving any adaptive procedure.