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

We consider adaptive finite element methods for second-order elliptic PDEs, where the arising discrete systems are not solved exactly. For contractive iterative solvers, we formulate an algorithm which monitors and steers mesh-refinement as well inexact solution of systems. prove that proposed strategy leads to linear convergence with optimal algebraic rates. Unlike prior works, however, focus on rates respect overall computational costs. In explicit terms, thus guarantees quasi-optimal time. particular, our analysis covers problems, by optimally preconditioned CG method nonlinear problems strongly monotone nonlinearity linearized so-called Zarantonello iteration.