13 citations · 13 across the 5 of their papers we have counts for
8 papers · 1 filter
Functional a posteriori error estimates for boundary element methods
Stefan Kurz, Dirk Pauly, Dirk Praetorius +2
Functional error estimates are well-established tools for a posteriori error estimation and related adaptive mesh-refinement for the finite element method (FEM). The present work p…
Weak-strong uniqueness for the Landau-Lifshitz-Gilbert equation in micromagnetics
Giovanni Di Fratta, Michael Innerberger, Dirk Praetorius
We consider the time-dependent Landau-Lifshitz-Gilbert equation. We prove that each weak solution coincides with the (unique) strong solution, as long as the latter exists in time.…
Adaptive IGAFEM with optimal convergence rates: T-splines
Gregor Gantner, 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…
The saturation assumption yields optimal convergence of two-level adaptive BEM
Dirk Praetorius, Michele Ruggeri, Ernst P. Stephan
We consider the convergence of adaptive BEM for weakly-singular and hypersingular integral equations associated with the Laplacian and the Helmholtz operator in 2D and 3D. The loca…
Dörfler marking with minimal cardinality is a linear complexity problem
Carl-Martin Pfeiler, Dirk Praetorius
Most adaptive finite element strategies employ the Dörfler marking strategy to single out certain elements of a triangulation for…
Instance-optimal goal-oriented adaptivity
Michael Innerberger, Dirk Praetorius
We consider an adaptive finite element method with arbitrary but fixed polynomial degree , where adaptivity is driven by an edge-based residual error estimator. Based on t…