Goal-oriented adaptive finite element methods with optimal computational complexity

Abstract

We consider a linear symmetric and elliptic PDE and a linear goal functional. We design and analyze a goal-oriented adaptive finite element method, which steers the adaptive mesh-refinement as well as the approximate solution of the arising linear systems by means of a contractive iterative solver like the optimally preconditioned conjugate gradient method or geometric multigrid. We prove linear convergence of the proposed adaptive algorithm with optimal algebraic rates. Unlike prior work, we do not only consider rates with respect to the number of degrees of freedom but even prove optimal complexity, i.e., optimal convergence rates with respect to the total computational cost.

References in corpus (1)

• Rate optimality of adaptive finite element methods with respect to the overall computational costs

Cited by in corpus (4)

• A Posteriori Single- and Multi-Goal Error Control and Adaptivity for Partial Differential Equations
• Optimal complexity of goal-oriented adaptive FEM for nonsymmetric linear elliptic PDEs
• Plain convergence of goal-oriented adaptive FEM
• Stability of step size control based on a posteriori error estimates