5 papers
Convergence analysis of structure-preserving schemes for the multicomponent compressible Euler flows
Jaya Agnihotri, Philipp Ãffner
We present a convergence analysis of a finite volume (FV) scheme for the multicomponent compressible Euler system in the framework of dissipative weak (DW) solutions. DW solutions…
Convergence of a Finite Volume Scheme for the Navier-Stokes-Korteweg Model via Dissipative Solutions
Jan Giesselmann, Philipp Ãffner, Robert Sauerborn
We propose a concept of dissipative weak (DW) solutions for the Navier-Stokes-Korteweg (NSK) system and prove conditional convergence of a structure-preserving finite volume scheme…
A high-order, structure preserving scheme for the stochastic Galerkin shallow water equations -- unification and two-dimensional extension
Philipp Ãffner, Philipp Öffner, Per Pettersson +1
Recently, two independent research efforts have been made to study the stochastic Galerkin formulation of the shallow water equations. Bender and Öffner developed entropy-conservat…
Convergence analysis for a finite-volume scheme for the Euler- and Navier-Stokes-Korteweg system via energy-variational solutions
Thomas Eiter, Jan Giesselmann, Robert Lasarzik +2
We consider a structure-preserving finite-volume scheme for the Euler-Korteweg (EK) and Navier-Stokes-Korteweg (NSK) equations. We prove that its numerical solutions converge to en…
The Lax-Wendroff theorem for Patankar-type methods applied to hyperbolic conservation laws
Janina Bender, Thomas Izgin, Philipp Ãffner +1
For hyperbolic conservation laws, the famous Lax-Wendroff theorem delivers sufficient conditions for the limit of a convergent numerical method to be a weak (entropy) solution. Thi…