214 citations · 1.5k across the 65 of their papers we have counts for
15 papers · 1 filter
A surface finite element method for the Navier-Stokes equations on evolving surfaces
Veit Krause, Eric Kunze, Axel Voigt
We introduce a surface finite element method for the numerical solution of Navier-Stokes equations on evolving surfaces with a prescribed deformation of the surface in normal direc…
Derivation and simulation of a two-phase fluid deformable surface model
Elena Bachini, Veit Krause, Ingo Nitschke +1
We consider two-phase fluid deformable surfaces as model systems for biomembranes. Such surfaces are modeled by incompressible surface Navier-Stokes-Cahn-Hilliard-like equations wi…
A diffuse interface approach for vector-valued PDEs on surfaces
Michael Nestler, Axel Voigt
Approximating PDEs on surfaces by the diffuse interface approach allows us to use standard numerical tools to solve these problems. This makes it an attractive numerical approach.…
Degenerate area preserving surface Allen-Cahn equation and its sharp interface limit
Michal Benes, Miroslav Kolar, Jan M. Sischka +1
We consider formal matched asymptotics to show the convergence of a degenerate area preserving surface Allen-Cahn equation to its sharp interface limit of area preserving geodesic…
A numerical approach for fluid deformable surfaces with conserved enclosed volume
Veit Krause, Axel Voigt
We consider surface finite elements and a semi-implicit time stepping scheme to simulate fluid deformable surfaces. Such surfaces are modeled by incompressible surface Navier-Stoke…
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…