The Mathematical Institute, University of Oxford, Eprints Archive

Analysis of Adjoint Error Correction for Superconvergent Functional Estimates

Giles, M. B. and Pierce, Niles A. (2001) Analysis of Adjoint Error Correction for Superconvergent Functional Estimates. Technical Report. Unspecified. (Submitted)

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Abstract

Earlier work introduced the notion of adjoint error correction for obtaining superconvergent estimates of functional outputs from approximate PDE solutions. This idea is based on a posteriori error analysis suggesting that the leading order error term in the functional estimate can be removed by using an adjoint PDE solution to reveal the sensitivity of the functional to the residual error in the original PDE solution. The present work provides a priori error analysis that correctly predicts the behaviour of the remaining leading order error term. Furthermore, the discussion is extended from the case of homogeneous boundary conditions and bulk functionals, to encompass the possibilities of inhomogeneous boundary conditions and boundary functionals. Numerical illustrations are provided for both linear and nonlinear problems.

This research was supported by EPSRC under grant GR/K91149, and by NASA/Ames Cooperative Agreement No. NCC 2-5431.

Item Type:Technical Report (Technical Report)
Subjects:D - G > Fluid mechanics
H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1237
Deposited By:Lotti Ekert
Deposited On:20 May 2011 09:19
Last Modified:20 May 2011 09:19

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