54 citations · 71 across the 8 of their papers we have counts for
9 papers
A Structure Preserving Finite Volume Scheme for the Navier-Stokes-Korteweg Equations
Jan Giesselmann, Philipp Öffner, Robert Sauerborn
We present a semi-discrete finite volume scheme for the local NavierStokes-Korteweg and Euler-Korteweg systems. Our scheme is applicable for equidistant Cartesian meshes in one and…
Discontinuous Galerkin methods for the complete stochastic Euler equations
Dominic Breit, Thamsanqa Castern Moyo, Philipp Öffner
In recent years, stochastic effects have become increasingly relevant for describing fluid behaviour, particularly in the context of turbulence. The most important model for invisc…
Energy-stable global radial basis function methods on summation-by-parts form
Jan Glaubitz, Jan Nordström, Philipp Öffner
Radial basis function methods are powerful tools in numerical analysis and have demonstrated good properties in many different simulations. However, for time-dependent partial diff…
Convergence of Discontinuous Galerkin Schemes for the Euler Equations via Dissipative Weak Solutions
Mária Lukácová-Medvidová, Philipp Öffner
In this paper, we present convergence analysis of high-order finite element based methods, in particular, we focus on a discontinuous Galerkin scheme using summation-by-parts opera…
Towards Stable Radial Basis Function Methods for Linear Advection Problems
Jan Glaubitz, Elise Le Mélédo, Philipp Öffner
In this work, we investigate (energy) stability of global radial basis function (RBF) methods for linear advection problems. Classically, boundary conditions (BC) are enforced stro…
Analysis of the SBP-SAT Stabilization for Finite Element Methods Part II: Entropy Stability
Rémi Abgrall, Jan Nordström, Philipp Öffner +1
In the research community, there exists the strong belief that a continuous Galerkin scheme is notoriously unstable and additional stabilization terms have to be added to guarantee…