activity
20192025
most citedA short note on plain convergence of adaptive least-squares finite element methods

13 citations · 13 across the 5 of their papers we have counts for

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Showing 2019Show all

8 papers · 1 filter

math.NA2019

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…

math.AP2019

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.…

math.NA2019

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…

math.NA2019

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…

math.NA2019

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…

math.NA2019

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…