## Adjoint Recovery of Superconvergent Functionals from Approximate Solutions of Partial Differential Equations (1998)

Citations: | 53 - 9 self |

### BibTeX

@TECHREPORT{Pierce98adjointrecovery,

author = {Niles A. Pierce and Michael B. Giles},

title = {Adjoint Recovery of Superconvergent Functionals from Approximate Solutions of Partial Differential Equations},

institution = {},

year = {1998}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract. Motivated by applications in computational fluid dynamics, a method is presented for obtaining estimates of integral functionals, such as lift or drag, that have twice the order of accuracy of the computed flow solution on which they are based. This is achieved through error analysis that uses an adjoint PDE to relate the local errors in approximating the flow solution to the corresponding global errors in the functional of interest. Numerical evaluation of the local residual error together with an approximate solution to the adjoint equations may thus be combined to produce a correction for the computed functional value that yields the desired improvement in accuracy. Numerical results are presented for the Poisson equation in one and two dimensions and for the nonlinear quasi-one-dimensional Euler equations. The theory is equally applicable to nonlinear equations in complex multidimensional domains and holds great promise for use in a range of engineering disciplines in which a few integral quantities are a key output of numerical approximations. Key words. PDEs, adjoint equations, error analysis, superconvergence AMS subject classifications. 65G99, 76N15 PII. S0036144598349423

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Citation Context ...the scatteredseld emanating from an aircraft. The amplitude of the wave propagating in a particular direction can be evaluated by a convolution integral over a closed surface surrounding the aircraft =-=[8, 21]-=-. Similar convolution integrals are used in the analysis of multi-port electromagnetic devices such as microwave ovens and EMR body scanners to evaluate radiation, transmission and re ection coecients... |

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Adaptive error control for element approximations of the lift and drag in a viscous
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aerodynamic design using control theory
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1 |
Two topics in nonlinear stability, in Adv
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