3 papers
math.NA2026
Adaptive finite element methods with optimally preconditioned GMRES guarantee optimal complexity
Thomas Führer, Paula Hilbert, Ani Miraçi +1
We analyze optimal complexity of adaptive finite element methods (AFEMs) for general second-order linear elliptic partial differential equations (PDEs) in the Lax-Milgram setting.…
math.NA2026
Generalized preconditioned conjugate gradients for adaptive FEM with optimal complexity
Paula Hilbert, Ani Miraçi, Dirk Praetorius
We consider adaptive finite element methods (AFEMs) with inexact algebraic solvers for second-order symmetric linear elliptic diffusion problems. Optimal complexity of AFEM, i.e.,…
math.NA2026
Multigoal-oriented adaptive finite element method with convergence rates
Roland Becker, Maximilian Brunner, Paula Hilbert +2
We formulate and analyze a goal-oriented adaptive finite element method for a symmetric linear elliptic partial differential equation (PDE) that can simultaneously deal with multip…