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Goal-oriented error estimation and adaptivity for the finite element method. (English) Zbl 0987.65110
The authors present an analysis for an a posteriori error estimate with respect to a class of elliptic boundary value problems. A new concept of goal oriented adaptivity is introduced and upper and lower bounds are established. Finally, a number of numerical experiments are performed which clearly show the reliability of the bounds in terms of global energy estimates.

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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