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.NA2025
A posteriori analysis of neural network approximations
Thomas Führer, Sergio Rojas
In a general setting, we study a posteriori estimates used in finite element analysis to measure the error between a solution and its approximation. The latter is not necessarily g…
math.NA2024
Aubin--Nitsche-type estimates for space-time FOSLS for parabolic PDEs
Thomas Führer, Gregor Gantner
We develop Aubin--Nitsche-type estimates for recently proposed first-order system least-squares finite element methods (FOSLS) for the heat equation. Under certain assumptions, whi…