12 citations · 17 across the 4 of their papers we have counts for
7 papers · 1 filter
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…
Analysis of the SBP-SAT Stabilization for Finite Element Methods Part I: Linear Problems
Rémi Abgrall, Jan Nordström, Philipp Öffner +1
In the hyperbolic community, discontinuous Galerkin approaches are mainly applied when finite element methods are considered. As the name suggested, the DG framework allows a disco…
General polytopal H(div) conformal finite elements and their discretisation spaces
Rémi Abgrall, Élise Le Mélédo, Philipp Öffner
We present a class of discretisation spaces and H(div)-conformal elements that can be built on any polytope. Bridging the flexibility of the Virtual Element spaces towards the elem…