Explanipedia

Characteristic boundary conditions for Hybridizable Discontinuous Galerkin methods Open

Jan Ellmenreich, Matteo Giacomini, Antonio Huerta, Philip L. Lederer · 2025

In this work we introduce the concept of characteristic boundary conditions (CBCs) within the framework of Hybridizable Discontinuous Galerkin (HDG) methods, including both the Navier-Stokes characteristic boundary conditions (NSCBCs) and …

High-order discretized ACMS method for the simulation of finite-size two-dimensional photonic crystals Open

Elena Giammatteo, Alexander Heinlein, Philip L. Lederer, Matthias Schlottbom · 2025

A bound-preserving and conservative enriched Galerkin method for elliptic problems Open

Gabriel R. Barrenechea, Philip L. Lederer, Andreas Rupp · 2025

We propose a locally conservative enriched Galerkin scheme that respects the discrete maximum principle of an elliptic problem. To this end, we use a substantial over-penalization of the discrete solution's jumps to obtain optimal converge…

Evaporating sessile droplets: solutal Marangoni effects overwhelm thermal Marangoni flow Open

Duarte Rocha, Philip L. Lederer, Pim J. Dekker, Alvaro Marin, Detlef Lohse , et al. · 2025

When an evaporating water droplet is deposited on a thermally conductive substrate, the minimum temperature will be at the apex due to evaporative cooling. Consequently, density and surface tension gradients emerge within the droplet and a…

On positivity preservation of hybrid discontinuous Galerkin methods on hypergraphs Open

Petr Knobloch, Philip L. Lederer, Andreas Rupp · 2025

Hybrid finite element methods, particularly hybridized discontinuous Galerkin (HDG) methods, are efficient numerical schemes for discretizing the diffusion equation, which encompasses two main physical principles: mass conservation and pos…

Embedded Trefftz DG framework for the analysis of discretizations with local-global decompositions Open

Philip L. Lederer, Christoph Lehrenfeld, Paul Stocker, Igor Voulis · 2024

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 comprehensive error analysis for the embedded Trefftz discontinuous G…

Evaporating sessile droplets: solutal Marangoni effects overwhelm thermal Marangoni flow Open

Duarte Rocha, Philip L. Lederer, Pim J. Dekker, Alvaro Marin, Detlef Lohse , et al. · 2024

When an evaporating water droplet is deposited on a thermally conductive substrate, the minimum temperature will be at the apex due to evaporative cooling. Consequently, density and surface tension gradients emerge within the droplet and a…

High-order discretized ACMS method for the simulation of finite-size two-dimensional photonic crystals Open

Elena Giammatteo, Alexander Heinlein, Philip L. Lederer, Matthias Schlottbom · 2024

The computational complexity and efficiency of the approximate mode component synthesis (ACMS) method is investigated for the two-dimensional heterogeneous Helmholtz equations, aiming at the simulation of large but finite-size photonic cry…

High-order projection-based upwind method for simulation of transitional turbulent flows Open

Philip L. Lederer, Xaver Mooslechner, Joachim Schöberl · 2024

We present a scalable, high-order implicit large-eddy simulation (ILES) approach for incompressible transitional flows. This method employs the mass-conserving mixed stress (MCS) method for discretizing the Navier-Stokes equations. The MCS…

Gradient-Robust Hybrid DG Discretizations for the Compressible Stokes Equations Open

Philip L. Lederer, Christian Merdon · 2024

This paper studies two hybrid discontinuous Galerkin (HDG) discretizations for the velocity-density formulation of the compressible Stokes equations with respect to several desired structural properties, namely provable convergence, the pr…

Trefftz discontinuous Galerkin discretization for the Stokes problem Open

Philip L. Lederer, Christoph Lehrenfeld, Paul Stocker · 2024

We introduce a new discretization based on a polynomial Trefftz-DG method for solving the Stokes equations. Discrete solutions of this method fulfill the Stokes equations pointwise within each element and yield element-wise divergence-free…

A discontinuous Galerkin approach for atmospheric flows with implicit condensation Open

Sabine Doppler, Philip L. Lederer, Joachim Schöberl, Henry von Wahl · 2023

We present a discontinuous Galerkin method for moist atmospheric dynamics, with and without warm rain. By considering a combined density for water vapour and cloud water, we avoid the need to model and compute a source term for condensatio…

Gradient-robust hybrid DG discretizations for the compressible Stokes equations Open

Philip L. Lederer, Christian Merdon · 2023

This paper studies two hybrid discontinuous Galerkin (HDG) discretizations for the velocity-density formulation of the compressible Stokes equations with respect to several desired structural properties, namely provable convergence, the pr…

Computational results for the work "Gradient-robust hybrid DG discretizations for the compressible Stokes equations" Open

Philip L. Lederer, Christian Merdon · 2023

Computational results for the work "Gradient-robust hybrid DG discretizations for the compressible Stokes equations" Open

Philip L. Lederer, Christian Merdon · 2023

High-order projection-based upwind method for implicit large eddy simulation Open

Philip L. Lederer, Xaver Mooslechner, Joachim Schöberl · 2023

We assess the ability of three different approaches based on high-order discontinuous Galerkin methods to simulate under-resolved turbulent flows. The capabilities of the mass conserving mixed stress method as structure resolving large edd…

Trefftz Discontinuous Galerkin discretization for the Stokes problem Open

Philip L. Lederer, Christoph Lehrenfeld, Paul Stocker · 2023

We introduce a new discretization based on the Trefftz-DG method for solving the Stokes equations. Discrete solutions of a corresponding method fulfill the Stokes equation pointwise within each element and yield element-wise divergence-fre…

A discontinuous Galerkin approach for atmospheric flows with implicit condensation Open

Sabine Doppler, Philip L. Lederer, Joachim Schöberl, Henry von Wahl · 2023

We present a discontinuous Galerkin method for moist atmospheric dynamics, with and without warm rain. By considering a combined density for water vapour and cloud water, we avoid the need to model and compute a source term for condensatio…

Asymptotically exact a posteriori error estimates for the BDM finite element approximation of mixed Laplace eigenvalue problems Open

Philip L. Lederer · 2023

We derive optimal and asymptotically exact a posteriori error estimates for the approximation of the eigenfunction of the Laplace eigenvalue problem. To do so, we combine two results from the literature. First, we use the hypercircle techn…

Divergence-Conforming Velocity and Vorticity Approximations for Incompressible Fluids Obtained with Minimal Facet Coupling Open

Jay Gopalakrishnan, Lukas Kogler, Philip L. Lederer, Joachim Schöberl · 2023

A conforming auxiliary space preconditioner for the mass conserving stress‐yielding method Open

Lukas Kogler, Philip L. Lederer, Joachim Schöberl · 2023

Summary We are studying the efficient solution of the system of linear equations stemming from the mass conserving stress‐yielding (MCS) discretization of the Stokes equations. We perform static condensation to arrive at a system for the p…

Computational results and python files for the work "Divergence-conforming velocity and vorticity approximations for incompressible fluids obtained with minimal facet coupling" Open

Philip L. Lederer, Lukas Kogler, Jay Gopalakrishnan, Joachim Schöberl · 2023

This repository contains data accompanying the paper "Divergence-conforming velocity and vorticity approximations for incompressible fluids obtained with minimal facet coupling". The implementation is based on the python-interface of the …

Computational results and python files for the work "Divergence-conforming velocity and vorticity approximations for incompressible fluids obtained with minimal facet coupling" Open

Philip L. Lederer, Lukas Kogler, Jay Gopalakrishnan, Joachim Schöberl · 2023

This repository contains data accompanying the paper "Divergence-conforming velocity and vorticity approximations for incompressible fluids obtained with minimal facet coupling". The implementation is based on the python-interface of the …

High-order projection-based upwind method for implicit large eddy simulation Open

Philip L. Lederer, Xaver Mooslechner, Joachim Schöberl · 2023

We assess the ability of three different approaches based on high-order discontinuous Galerkin methods to simulate under-resolved turbulent flows. The capabilities of the mass conserving mixed stress method as structure resolving large edd…

Mixed finite elements for Bingham flow in a pipe Open

Tom Gustafsson, Philip L. Lederer · 2022

We consider mixed finite element approximations of viscous, plastic Bingham flow in a cylindrical pipe. A novel a priori and a posteriori error analysis is introduced which is based on a discrete mesh dependent norm for the normalized Lagr…

A conforming auxiliary space preconditioner for the mass conserving mixed stress method Open

Lukas Kogler, Philip L. Lederer, Joachim Schöberl · 2022

We are studying the efficient solution of the system of linear equation stemming from the mass conserving mixed stress (MCS) method discretization of the Stokes equations. To that end we perform static condensation to arrive at a system fo…

Analysis of Weakly Symmetric Mixed Finite Elements for Elasticity Open

Philip L. Lederer, Rolf Stenberg · 2022

We consider mixed finite element methods for linear elasticity where the symmetry of the stress tensor is weakly enforced. Both an a priori and a posteriori error analysis are given for several known families of methods that are uniformly …

Mixed finite elements for Bingham flow in a pipe Open

Tom Gustafsson, Philip L. Lederer · 2022

We consider mixed finite element approximations of viscous, plastic Bingham flow in a cylindrical pipe. A novel a priori and a posteriori error analysis is introduced which is based on a discrete mesh dependent norm for the normalized Lagr…

Hybridized Discontinuous Galerkin Methods for a Multiple Network Poroelasticity Model with Medical Applications Open

Johannes Kraus, Philip L. Lederer, Maria Lymbery, Kevin Osthues, Joachim Schöberl · 2022

The quasi-static multiple network poroelastic theory (MPET) model, first introduced in the context of geomechanics, has recently found new applications in medicine. In practice, the parameters in the MPET equations can vary over several or…

A note on asymptotically exact a posteriori error estimates for mixed Laplace eigenvalue problems Open

Philip L. Lederer · 2022

We derive optimal and asymptotically exact a posteriori error estimates for the approximation of the Laplace eigenvalue problem. To do so, we combine two results from the literature. First, we use the hypercircle techniques developed for m…

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