118 citations · 565 across the 34 of their papers we have counts for
6 papers · 1 filter
Fully well-balanced entropy controlled discontinuous Galerkin spectral element method for shallow water flows: global flux quadrature and cell entropy correction
Yogiraj Mantri, Philipp Öffner, Mario Ricchiuto
We present a novel approach for solving the shallow water equations using a discontinuous Galerkin spectral element method. The method we propose has three main features. First, it…
A new variable shape parameter strategy for RBF approximation using neural networks
Fatemeh Nassajian Mojarrad, Maria Han Veiga, Jan S. Hesthaven +1
The choice of the shape parameter highly effects the behaviour of radial basis function (RBF) approximations, as it needs to be selected to balance between ill-condition of the int…
On the convergence of residual distribution schemes for the compressible Euler equations via dissipative weak solutions
Rémi Abgrall, Mária Lukácova-Medvid'ová, Philipp Öffner
In this work, we prove the convergence of residual distribution schemes to dissipative weak solutions of the Euler equations. We need to guarantee that the residual distribution sc…
High order entropy preserving ADER scheme
Elena Gaburro, Philipp Öffner, Mario Ricchiuto +1
In this paper, we develop a fully discrete entropy preserving ADER-Discontinuous Galerkin (ADER-DG) method. To obtain this desired result, we equip the space part of the method wit…
A study of the local dynamics of modified Patankar DeC and higher order modified Patankar RK methods
Thomas Izgin, Philipp Öffner
Patankar schemes have attracted increasing interest in recent years because they preserve the positivity of the analytical solution of a production-destruction system (PDS) irrespe…
Summation-by-parts operators for general function spaces
Jan Glaubitz, Jan Nordström, Philipp Öffner
Summation-by-parts (SBP) operators are popular building blocks for systematically developing stable and high-order accurate numerical methods for time-dependent differential equati…