Abstract
This paper is concerned with the computation of numerical discretization error for uncertainty quantification. An a posteriori error formula is described for a functional measurement of the solution to a scalar advection equation that is estimated by finite volume approximations. An exact error formula and computable error estimate are derived based on an abstractly defined approximation of the adjoint solution. The adjoint problem is divorced from the finite volume method used to approximate the forward solution variables and may be approximated using a low-order finite volume method. The accuracy of the computable error estimate provably satisfies an a priori error bound for sufficiently smooth solutions of the forward and adjoint problems. Computational examples are provided that show support of the theory for smooth solutions. The application to problems with discontinuities is also investigated computationally.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
