10 papers · 1 filter
Dissipation-preserving discretization of the Cahn--Hilliard equation with dynamic boundary conditions
R. Altmann, C. Zimmer
This paper deals with time stepping schemes for the Cahn--Hilliard equation with three different types of dynamic boundary conditions. The proposed schemes of first and second orde…
Bulk-surface Lie splitting for parabolic problems with dynamic boundary conditions
Robert Altmann, Balázs Kovács, Christoph Zimmer
This paper studies bulk-surface splitting methods of first order for (semi-linear) parabolic partial differential equations with dynamic boundary conditions. The proposed Lie split…
A decoupling and linearizing discretization for weakly coupled poroelasticity with nonlinear permeability
Robert Altmann, Roland Maier
We analyze a semi-explicit time discretization scheme of first order for poro\-elasticity with nonlinear permeability provided that the elasticity model and the flow equation are o…
Continuous Galerkin Schemes for Semi-Explicit Differential-Algebraic Equations
Robert Altmann, Roland Herzog
This paper studies a new class of integration schemes for the numerical solution of semi-explicit differential-algebraic equations of differentiation index 2 in Hessenberg form. Ou…
A multiscale method for heterogeneous bulk-surface coupling
Robert Altmann, Barbara Verfürth
In this paper, we construct and analyze a multiscale (finite element) method for parabolic problems with heterogeneous dynamic boundary conditions. As origin, we consider a reformu…
Semi-explicit discretization schemes for weakly-coupled elliptic-parabolic problems
Robert Altmann, Roland Maier, Benjamin Unger
We prove first-order convergence of the semi-explicit Euler scheme combined with a finite element discretization in space for elliptic-parabolic problems which are weakly coupled.…