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The certified descent algorithm (CDA) is a gradient-based method for shapeoptimization which certifies that the direction computed using the shapegradient is a genuine descent direction for the objective functional underanalysis. It relies on the computation of an upper bound of the errorintroduced by the finite element approximation of the shape gradient. In thispaper, we present a goal-oriented error estimator which depends solely on localquantities and is fully-computable. By means of the equilibrated fluxesapproach, we construct a unified strategy valid for both conforming finiteelement approximations and discontinuous Galerkin discretizations. The newvariant of the CDA is tested on the inverse identification problem ofelectrical impedance tomography: both its ability to identify a genuine descentdirection at each iteration and its reliable stopping criterion are confirmed.

journal of scientific computing

An equilibrated fluxes approach to the certified descent algorithm for  shape optimization using conforming finite element and discontinuous Galerkin  discretizations