76 citations · 1.5k across the 82 of their papers we have counts for
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Convergent tangent plane integrators for the simulation of chiral magnetic skyrmion dynamics
Gino Hrkac, Carl-Martin Pfeiler, Dirk Praetorius +3
We consider the numerical approximation of the Landau-Lifshitz-Gilbert equation, which describes the dynamics of the magnetization in ferromagnetic materials. In addition to the cl…
Linear second-order IMEX-type integrator for the (eddy current) Landau-Lifshitz-Gilbert equation
Giovanni Di Fratta, Carl-Martin Pfeiler, Dirk Praetorius +2
Combining ideas from [Alouges et al. (Numer. Math., 128, 2014)] and [Praetorius et al. (Comput. Math. Appl., 2017)], we propose a numerical algorithm for the integration of the non…
Adaptive vertex-centered finite volume methods for general second-order linear elliptic PDEs
Christoph Erath, Dirk Praetorius
We prove optimal convergence rates for the discretization of a general second-order linear elliptic PDE with an adaptive vertex-centered finite volume scheme. While our prior work…
A linear Uzawa-type solver for nonlinear transmission problems
Thomas Führer, Dirk Praetorius
We propose an Uzawa-type iteration for the Johnson-Nédélec formulation of a Laplace-type transmission problem with possible (strongly monotone) nonlinearity in the interior domain.…
Adaptive IGAFEM with optimal convergence rates: Hierarchical B-splines
Gregor Gantner, Daniel Haberlik, Dirk Praetorius
We consider an adaptive algorithm for finite element methods for the isogeometric analysis (IGAFEM) of elliptic (possibly non-symmetric) second-order partial differential equations…