3 papers
math.NA2025
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…
math.NA2025
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…
math.NA2024
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…