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On goal-oriented error estimation for elliptic problems: Application to the control of pointwise errors. (English) Zbl 0945.65123

The authors present a theory of goal-oriented error estimation. It involves the computation of an influence function for each quantity of interest. The influence function which is obtained as the solution of a dual problem indicates how the residual error influences the error in the particular measure. The performance of the method is shown on a one-dimensional problem.

MSC:

65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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