13 citations · 13 across the 5 of their papers we have counts for
13 papers · 1 filter
The mass-lumped midpoint scheme for computational micromagnetics: Newton linearization and application to magnetic skyrmion dynamics
Giovanni Di Fratta, Carl-Martin Pfeiler, Dirk Praetorius +1
We discuss a mass-lumped midpoint scheme for the numerical approximation of the Landau-Lifshitz-Gilbert equation, which models the dynamics of the magnetization in ferromagnetic ma…
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…
Optimal convergence rates for goal-oriented FEM with quadratic goal functional
Roland Becker, Michael Innerberger, Dirk Praetorius
We consider a linear elliptic PDE and a quadratic goal functional. The goal-oriented adaptive FEM algorithm (GOAFEM) solves the primal as well as a dual problem, where the goal fun…