Goal-oriented adaptive finite element method for semilinear elliptic PDEs

12/13/2021

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by   Roland Becker, et al.

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We formulate and analyze a goal-oriented adaptive finite element method (GOAFEM) for a semilinear elliptic PDE and a linear goal functional. The strategy involves the finite element solution of a linearized dual problem, where the linearization is part of the adaptive strategy. Linear convergence and optimal algebraic convergence rates are shown.