6 papers · 1 filter
IMEX Schemes for Compressible Flow using Hybridizable Discontinuous Galerkin Methods
Jan Ellmenreich, Edmond K. Shehadi, Philip L. Lederer
In this work, we develop a geometry-split implicit-explicit (IMEX) framework for the compressible flow equations, wherein stiff regions are treated via an implicit hybridizable dis…
A bound-preserving and conservative enriched Galerkin method for elliptic problems
Gabriel R. Barrenechea, Philip L. Lederer, Andreas Rupp
We propose a locally conservative enriched Galerkin scheme that preserves the physical bounds for an elliptic problem. To this end, we use a substantial over-penalization of the di…
Embedded Trefftz DG framework for the analysis of discretizations with local-global decompositions
Philip L. Lederer, Christoph Lehrenfeld, Paul Stocker +1
This paper presents a framework for the analysis of discretization methods based on the decomposition into local and global problems. We apply the framework to provide a comprehens…
On positivity preservation of hybrid discontinuous Galerkin methods on hypergraphs
Petr Knobloch, Philip L. Lederer, Andreas Rupp
Hybrid finite element methods, particularly hybridized discontinuous Galerkin (HDG) methods, are efficient numerical schemes for discretizing the diffusion equation, which encompas…
Characteristic boundary conditions for Hybridizable Discontinuous Galerkin methods
Jan Ellmenreich, Matteo Giacomini, Antonio Huerta +1
In this work we introduce the concept of characteristic boundary conditions (CBCs) within the framework of Hybridizable Discontinuous Galerkin (HDG) methods, including both the Nav…
High-order discretized ACMS method for the simulation of finite-size two-dimensional photonic crystals
Elena Giammatteo, Alexander Heinlein, Philip Lukas Lederer +1
The computational complexity and efficiency of the approximate mode component synthesis (ACMS) method is investigated for the two-dimensional heterogeneous Helmholtz equations, aim…