An application of the averaged gradient technique. (English) Zbl 1201.65205

Chleboun, Jan

Chleboun, J. (ed.) et al., Programs and algorithms of numerical mathematics 14. Proceedings of the seminar, DolníMaxov, Czech Republic, June 1–6, 2008. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics (ISBN 978-80-85823-55-4). 65-70 (2008).

From the introduction: Gradient averaging (also known as gradient recovery) is a technique for improving the accuracy of an approximate gradient obtained via a numerical method. Sensitivity analysis deals with analyzing the response of a function (or a functional) a small perturbation of its input values. In this contribution, we limit ourselves to gradients originating from finite element solutions of boundary value problems and to criterion-functionals that evaluate these solutions. Our goal is to show that the use of a gradient recovery technique in sensitivity analysis formulae can result in a better assessment of the quality of approximate minimizers of criterion-functionals that appear in parameter identification problems or the worst scenario method, for example.
For the entire collection see [Zbl 1194.65013].

MSC:

65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25	Boundary value problems for second-order elliptic equations
65N21	Numerical methods for inverse problems for boundary value problems involving PDEs
35R30	Inverse problems for PDEs

Keywords:

parameter identification; gradient averaging; gradient recovery; sensitivity analysis; finite element