32 citations · 69 across the 10 of their papers we have counts for
12 papers
Finite Volume Convergence for a Heat Equation with a Measure-Valued Source
Matthias Gobbert, Martin Kruž\'ık, Andreas Meister +1
Past work with Tom Seidman analyzed the spatial convergence order of the numerical finite element method applied to time-dependent diffusion-reaction equations with a measure-value…
Order conditions for Runge--Kutta-like methods with solution-dependent coefficients
Thomas Izgin, David I. Ketcheson, Andreas Meister
In recent years, many positivity-preserving schemes for initial value problems have been constructed by modifying a Runge--Kutta (RK) method by weighting the right-hand side of the…
On the Dynamics of First and Second Order GeCo and gBBKS Schemes
Thomas Izgin, Stefan Kopecz, Angela Martiradonna +1
In this paper we investigate the stability properties of the so-called gBBKS and GeCo methods, which belong to the class of nonstandard schemes and preserve the positivity as well…
A Stability Analysis of Modified Patankar-Runge-Kutta methods for a nonlinear Production-Destruction System
Thomas Izgin, Stefan Kopecz, Andreas Meister
Modified Patankar-Runge-Kutta (MPRK) methods preserve the positivity as well as conservativity of a production-destruction system (PDS) of ordinary differential equations for all t…
On the stability of strong-stability-preserving modified Patankar Runge-Kutta schemes
Juntao Huang, Thomas Izgin, Stefan Kopecz +2
In this paper, we perform stability analysis for a class of second and third order accurate strong-stability-preserving modified Patankar Runge-Kutta (SSPMPRK) schemes, which were…
A Meshfree Point Collocation Method for Elliptic Interface Problems
Heinrich Kraus, Jörg Kuhnert, Andreas Meister +1
We present a meshfree generalized finite difference method for solving Poisson's equation with a diffusion coefficient that contains jump discontinuities up to several orders of ma…
On the Stability of Unconditionally Positive and Linear Invariants Preserving Time Integration Schemes
Thomas Izgin, Stefan Kopecz, Andreas Meister
Higher-order time integration methods that unconditionally preserve the positivity and linear invariants of the underlying differential equation system cannot belong to the class o…
On Lyapunov Stability of Positive and Conservative Time Integrators and Application to Second Order Modified Patankar--Runge--Kutta Schemes
Thomas Izgin, Stefan Kopecz, Andreas Meister
Since almost twenty years, modified Patankar--Runge--Kutta (MPRK) methods have proven to be efficient and robust numerical schemes that preserve positivity and conservativity of th…
Unconditionally Positive and Conservative Third Order Modified Patankar-Runge-Kutta Discretizations of Production-Destruction Systems
Stefan Kopecz, Andreas Meister
Modified Patankar-Runge-Kutta (MPRK) schemes are numerical methods for the solution of positive and conservative production-destruction systems. They adapt explicit Runge-Kutta sch…
On Order Conditions for modified Patankar-Runge-Kutta schemes
Stefan Kopecz, Andreas Meister
In \cite{BDM2003} the modified Patankar-Euler and modified Patankar-Runge-Kutta schemes were introduced to solve positive and conservative systems of ordinary differential equation…
Fast Solvers for Unsteady Thermal Fluid Structure Interaction
Philipp Birken, Tobias Gleim, Detlef Kuhl +1
We consider time dependent thermal fluid structure interaction. The respective models are the compressible Navier-Stokes equations and the nonlinear heat equation. A partitioned co…
Finite volume approach for the instationary Cosserat rod model describing the spinning of viscous jets
Walter Arne, Nicole Marheineke, Andreas Meister +1
The spinning of slender viscous jets can be described asymptotically by one-dimensional models that consist of systems of partial and ordinary differential equations. Whereas the w…