Instance-optimal goal-oriented adaptivity

Abstract

We consider an adaptive finite element method with arbitrary but fixed polynomial degree $p\ge 1$, where adaptivity is driven by an edge-based residual error estimator. Based on the modified maximum criterion from [Diening et al, Found. Comput. Math. 16, 2016], we propose a goal-oriented adaptive algorithm and prove that it is instance optimal. More precisely, the goal-error is bounded by the product of the total errors (being the sum of energy error plus data oscillations) of the primal and the dual problem, and the proposed algorithm is instance optimal with respect to this upper bound. Numerical experiments underline our theoretical findings.

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Cited by in corpus (3)

• MooAFEM: An object oriented Matlab code for higher-order adaptive FEM for (nonlinear) elliptic PDEs
• Plain convergence of adaptive algorithms without exploiting reliability and efficiency
• Plain convergence of goal-oriented adaptive FEM