Publication Results

Code: MOX 68
Title: Nested dual-residual a posteriori error estimators for advection-diffusion-reaction problems
Date: Wednesday 7th September 2005
Author(s) : Micheletti, Stefano; Perotto, Simona
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Abstract: In this work we introduce a fully computable dual-based a posteriori error estimator for standard scalar advection-diffusion-reaction problems. In particular, such an estimator does not depend on neither the primal nor the dual exact solution, but only on the corresponding Galerkin finite element approximations. This new approach merges the main advantages of the dual-based and of the residual-based error analysis, being devised as a residual-based estimator nested in a dual-based one. This allows us to explicitly approximate suitable functionals of the solution, in the spirit of a classical goal-oriented analysis, at the same cost as a dual-based strategy, the solution of two differential problems being involved. The related issue of optimal mesh adaptivity is also addressed. Several two-dimensional numerical test cases validate the proposed theory as well as the employed adaptive procedure.