Goal-oriented adaptive finite element method for semilinear elliptic PDEs

Published 13 Dec 2021 in math.NA and cs.NA | (2112.06687v1)

Abstract: 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.

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