A posteriori estimates for errors of functionals on finite volume approximations to solutions of elliptic boundary value problems
Provides a framework for error estimation in finite volume methods, which is incremental for computational scientists using these discretizations.
Extended dual-weighted residual methods for a posteriori error estimation to node-centered finite volume discretizations of elliptic boundary value problems, enabling estimation of modeling and discretization errors with respect to user-defined functionals.
This article describes the extension of recent methods for a posteriori error estimation such as dual-weighted residual methods to node-centered finite volume discretizations of second order elliptic boundary value problems including upwind discretizations. It is shown how different sources of errors, in particular modeling errors and discretization errors, can be estimated with respect to a user-defined output functional.