50 citations · 71 across the 21 of their papers we have counts for
4 papers · 2 filters
Goal-Oriented Error Estimation and Adaptivity for Stochastic Collocation FEM
Alex Bespalov, Dirk Praetorius, Thomas Round +1
We propose and analyze a general goal-oriented adaptive strategy for approximating quantities of interest (QoIs) associated with solutions to linear elliptic partial differential e…
Iterative solvers in adaptive FEM
Philipp Bringmann, Ani Miraçi, Dirk Praetorius
This chapter provides an overview of state-of-the-art adaptive finite element methods (AFEMs) for the numerical solution of second-order elliptic partial differential equations (PD…
Unconditional full linear convergence and optimal complexity of adaptive iteratively linearized FEM for nonlinear PDEs
Ani Miraçi, Dirk Praetorius, Julian Streitberger
We propose an adaptive iteratively linearized finite element method (AILFEM) in the context of strongly monotone nonlinear operators in Hilbert spaces. The approach combines adapti…
Cost-optimal adaptive FEM with linearization and algebraic solver for semilinear elliptic PDEs
Maximilian Brunner, Dirk Praetorius, Julian Streitberger
We consider scalar semilinear elliptic PDEs, where the nonlinearity is strongly monotone, but only locally Lipschitz continuous. To linearize the arising discrete nonlinear problem…