13 citations · 13 across the 5 of their papers we have counts for
7 papers · 1 filter
Micromagnetics of thin films in the presence of Dzyaloshinskii-Moriya interaction
Elisa Davoli, Giovanni Di Fratta, Dirk Praetorius +1
In this paper, we study the thin-film limit of the micromagnetic energy functional in the presence of bulk Dzyaloshinskii-Moriya interaction (DMI). Our analysis includes both a sta…
Spin-diffusion model for micromagnetics in the limit of long times
Giovanni Di Fratta, Ansgar Jüngel, Dirk Praetorius +1
In this paper, we consider spin-diffusion Landau-Lifshitz-Gilbert equations (SDLLG), which consist of the time-dependent Landau-Lifshitz-Gilbert (LLG) equation coupled with a time-…
Energy contraction and optimal convergence of adaptive iterative linearized finite element methods
Pascal Heid, Dirk Praetorius, Thomas P. Wihler
We revisit a unified methodology for the iterative solution of nonlinear equations in Hilbert spaces. Our key observation is that the general approach from [Heid & Wihler, Math. Co…
Two-level a posteriori error estimation for adaptive multilevel stochastic Galerkin FEM
Alex Bespalov, Dirk Praetorius, Michele Ruggeri
The paper considers a class of parametric elliptic partial differential equations (PDEs), where the coefficients and the right-hand side function depend on infinitely many (uncerta…
A short note on plain convergence of adaptive least-squares finite element methods
Thomas Führer, Dirk Praetorius
We show that adaptive least-squares finite element methods driven by the canonical least-squares functional converge under weak conditions on PDE operator, mesh-refinement, and mar…
Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver
Alexander Haberl, Dirk Praetorius, Stefan Schimanko +1
We consider a second-order elliptic boundary value problem with strongly monotone and Lipschitz-continuous nonlinearity. We design and study its adaptive numerical approximation in…