33 citations · 59 across the 8 of their papers we have counts for
8 papers
Convergent numerical schemes for the viscoelastic Giesekus model in two dimensions
Endre Süli, Dennis Trautwein
In this work, we develop a class of stable and convergent numerical methods for the approximate solution of the viscoelastic Giesekus model in two space dimensions. The model coupl…
Structure-preserving parametric finite element methods for two-phase Stokes flow based on Lagrange multiplier approaches
Harald Garcke, Dennis Trautwein, Ganghui Zhang
We present a novel formulation for parametric finite element methods to approximate two-phase Stokes flow. The new formulation is based on the classical Stokes equation in the bulk…
On energy-dissipative finite element approximations for rate-type viscoelastic fluids with stress diffusion
Dennis Trautwein
We study a fully discrete finite element approximation of a model for unsteady flows of rate-type viscoelastic fluids with stress diffusion in two and three dimensions. The model c…
Parametric finite element approximation of two-phase Navier--Stokes flow with viscoelasticity
Harald Garcke, Robert Nürnberg, Dennis Trautwein
In this work, we present a parametric finite element approximation of two-phase Navier-Stokes flow with viscoelasticity. The free boundary problem is given by the viscoelastic Navi…
Approximation and existence of a viscoelastic phase-field model for tumour growth in two and three dimensions
Harald Garcke, Dennis Trautwein
In this work, we present a phase-field model for tumour growth, where a diffuse interface separates a tumour from the surrounding host tissue. In our model, we consider transport p…
On a diffuse interface model for incompressible viscoelastic two-phase flows
Yadong Liu, Dennis Trautwein
This paper concerns a diffuse interface model for the flow of two incompressible viscoelastic fluids in a bounded domain. More specifically, the fluids are assumed to be macroscopi…
Viscoelastic Cahn--Hilliard models for tumour growth
Harald Garcke, Balázs Kovács, Dennis Trautwein
We introduce a new phase field model for tumour growth where viscoelastic effects are taken into account. The model is derived from basic thermodynamical principles and consists of…
Numerical analysis for a Cahn-Hilliard system modelling tumour growth with chemotaxis and active transport
Harald Garcke, Dennis Trautwein
In this work, we consider a diffuse interface model for tumour growth in the presence of a nutrient which is consumed by the tumour. The system of equations consists of a Cahn--Hil…