Abstract The ability to efficiently solve topology optimization problems is of great importance for many practical applications. Hence, there a demand efficient solution algorithms. In this paper, we propose novel quasi-Newton methods solving PDE-constrained problems. Our approach based on and extends the popular algorithm Amstutz Andrä (J Comput Phys 216: 573–588, 2006). To do so, introduce ne...

In this paper, we propose a general smoothing Broyden-like quasi-Newton method for solving a class of nonsmooth equations. Under appropriate conditions, the proposed method converges to a solution of the equation globally and superlinearly. In particular, the proposed method provides the possibility of developing a quasi-Newton method that enjoys superlinear convergence even if strict complemen...

A rigorous convergence theory for Galerkin methods for a model Helmholtz problem in Rd, d ∈ {1, 2, 3} is presented. General conditions on the approximation properties of the approximation space are stated that ensure quasi-optimality of the method. As an application of the general theory, a full error analysis of the classical hp-version of the finite element method (hp-FEM) is presented for th...