You can manage bookmarks using lists, please log in to your user account for this.
Media type:
E-Article
Title:
A METHOD TO CALCULATE NUMERICAL ERRORS USING ADJOINT ERROR ESTIMATION FOR LINEAR ADVECTION
Contributor:
CONNORS, JEFFREY M.;
BANKS, JEFFREY W.;
HITTINGER, JEFFREY A.;
WOODWARD, CAROL S.
Published:
Society for Industrial and Applied Mathematics, 2013
Published in:
SIAM Journal on Numerical Analysis, 51 (2013) 2, Seite 894-926
Language:
English
DOI:
10.1137/110845100
ISSN:
0036-1429
Origination:
Footnote:
Description:
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.