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Sensitivity analysis of partial differential equations: A case for functional sensitivity
Author(s) -
Kabala Z. J.,
Milly P. C. D.
Publication year - 1991
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690070202
Subject(s) - sensitivity (control systems) , mathematics , finite element method , grid , partial differential equation , partial derivative , functional equation , representation (politics) , mathematical optimization , mathematical analysis , geometry , physics , electronic engineering , politics , political science , law , engineering , thermodynamics
Sensitivity analysis allows for analyzing the effects of parameter uncertainty. For functional parameters, the sensitivity of the system is described by the functional derivatives of the output variables with respect to the parameters. Approximation of each of the functional parameters by a finite number of scalars (via the finite element representation) allows one to use elementary sensitivity analysis. The functional sensitivities are easily approximated from elementary sensitivities and, being objective quantities, they allow one to evaluate the numerical quality of sensitivities. The grid density necessary for computing functional sensitivities may differ significantly from the grid required for the numerical solution of the governing equation.