94 citations · 439 across the 45 of their papers we have counts for
10 papers · 1 filter
Neural network based limiter with transfer learning
Maria Han Veiga, Rémi Abgrall
A neural network is trained using simulation data from a Runge Kutta discontinuous Galerkin (RKDG) method and a modal high order limiter. With this methodology, we design one and t…
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…
Non-equilibrium Model for Weakly Compressible Multi-component Flows: the Hyperbolic Operator
Barbara Re, Rémi Abgrall
We present a novel pressure-based method for weakly compressible multiphase flows, based on a non-equilibrium Baer and Nunziato-type model. In this work, we describe the hyperbolic…
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…
Reinterpretation and Extension of Entropy Correction Terms for Residual Distribution and Discontinuous Galerkin Schemes: Application to Structure Preserving Discretization
Rémi Abgrall, Philipp Öffner, Hendrik Ranocha
For the general class of residual distribution (RD) schemes, including many finite element (such as continuous/discontinuous Galerkin) and flux reconstruction methods, an approach…