54 citations · 414 across the 19 of their papers we have counts for
20 papers
Odd behaviour of even geometries: an explanation for superconvergent geometric consistency errors
Hanne Hardering, Simon Praetorius, Gentian Zavalani
Piecewise polynomial surface approximations used in surface finite element methods often seem to behave better than their standard approximation properties suggest if their polynom…
Surface Minkowski tensors to characterize shapes on curved surfaces
Lea Happel, Hanne Hardering, Simon Praetorius +1
We introduce surface Minkowski tensors to characterize rotational symmetries of shapes embedded in curved surfaces. The definition is based on a modified vector transport of the sh…
Active smectics on a sphere
Michael Nestler, Simon Praetorius, Zhi-Feng Huang +2
The dynamics of active smectic liquid crystals confined on a spherical surface is explored through an active phase field crystal model. Starting from an initially randomly perturbe…
Parametric Finite Element Discretization of the Surface Stokes Equations
Hanne Hardering, Simon Praetorius
We study a higher-order surface finite element (SFEM) penalty-based discretization of the tangential surface Stokes problem. Several discrete formulations are investigated which ar…
The influence of finite size particles on fluid velocity and transport though porous media
Mirko Residori, Simon Praetorius, Pietro de Anna +1
Understanding the coupling between flow, hydrodynamic transport and dispersion of colloids with finite-size in porous media is a long-standing challenge. This problem is relevant f…
Diffusion of tangential tensor fields: numerical issues and influence of geometric properties
Elena Bachini, Philip Brandner, Thomas Jankuhn +4
We study the diffusion of tangential tensor-valued data on curved surfaces. For this purpose, several finite-element-based numerical methods are collected and used to solve a tange…
Tangential Errors of Tensor Surface Finite Elements
Hanne Hardering, Simon Praetorius
We discretize a tangential tensor field equation using a surface-finite element approach with a penalization term to ensure almost tangentiality. It is natural to measure the quali…
Finite element discretization methods for velocity-pressure and stream function formulations of surface Stokes equations
Philip Brandner, Thomas Jankuhn, Simon Praetorius +2
In this paper we study parametric TraceFEM and parametric SurfaceFEM (SFEM) discretizations of a surface Stokes problem. These methods are applied both to the Stokes problem in vel…
Dune-CurvedGrid -- A Dune module for surface parametrization
Simon Praetorius, Florian Stenger
In this paper we introduce and describe an implementation of curved (surface) geometries within the Dune framework for grid-based discretizations. Therefore, we employ the abstract…
An efficient numerical framework for the amplitude expansion of the phase-field crystal model
Simon Praetorius, Marco Salvalaglio, Axel Voigt
The study of polycrystalline materials requires theoretical and computational techniques enabling multiscale investigations. The amplitude expansion of the phase field crystal mode…
Topological and geometrical quantities in active cellular structures
Dennis Wenzel, Simon Praetorius, Axel Voigt
Topological and geometrical properties and the associated topological defects find a rapidly growing interest in studying the interplay between mechanics and the collective behavio…
Active crystals on a sphere
Simon Praetorius, Axel Voigt, Raphael Wittkowski +1
Two-dimensional crystals on curved manifolds exhibit nontrivial defect structures. Here, we consider "active crystals" on a sphere, which are composed of self-propelled colloidal p…
Nematic liquid crystals on curved surfaces - a thin film limit
Ingo Nitschke, Michael Nestler, Simon Praetorius +2
We consider a thin film limit of a Landau-de Gennes Q-tensor model. In the limiting process we observe a continuous transition where the normal and tangential parts of the Q-tensor…
Orientational order on surfaces - the coupling of topology, geometry, and dynamics
Michael Nestler, Ingo Nitschke, Simon Praetorius +1
We consider the numerical investigation of surface bound orientational order using unit tangential vector fields by means of a gradient-flow equation of a weak surface Frank-Oseen…
A mesoscopic field theoretical approach for active systems
Francesco Alaimo, Simon Praetorius, Axel Voigt
We introduce a mesocopic modeling approach for active systems. The continuum model allows to consider microscopic details as well as emerging macroscopic behavior and can be consid…
Development and Analysis of a Block-Preconditioner for the Phase-Field Crystal Equation
Simon Praetorius, Axel Voigt
We develop a preconditioner for the linear system arising from a finite element discretization of the Phase Field Crystal (PFC) equation. The PFC model serves as an atomic descript…
Liquid crystalline growth within a phase-field crystal model
Sai Tang, Simon Praetorius, Rainer Backofen +3
By using a phase-field crystal (PFC) model, the liquid-crystal growth of the plastic triangular phase is simulated with emphasis on crystal shape and topological defect formation.…
A mechanism for cell motility by active polar gels
Wieland Marth, Simon Praetorius, Axel Voigt
We analyse a generic motility model, with the motility mechanism arising by contractile stress due to the interaction of myosin and actin. A hydrodynamic active polar gel theory is…
A Navier Stokes Phase Field Crystal Model for Colloidal Suspensions
Simon Praetorius, Axel Voigt
We develop a fully continuous model for colloidal suspensions with hydrodynamic interactions. The Navier Stokes Phase Field Crystal (NS-PFC) model combines ideas of dynamic density…
Structure and dynamics of interfaces between two coexisting liquid crystalline phases
Simon Praetorius, Axel Voigt, Raphael Wittkowski +1
The phase-field-crystal model is used to access the structure and thermodynamics of interfaces between two coexisting liquid crystalline phases in two spatial dimensions. Depending…