44 citations · 124 across the 26 of their papers we have counts for
29 papers
Embedded Trefftz DG method for steady Navier-Stokes flow. Part I: Oseen linearization
Paul Stocker, Igor Voulis, Christoph Lehrenfeld +1
We develop an embedded Trefftz-DG method for the Oseen problem and prove a complete stability and quasi-optimality theory in standard DG norms. The key ingredient is a construction…
Embedded Trefftz DG method for steady Navier-Stokes flow. Part II: Nonlinear problem
Paul Stocker, Igor Voulis, Christoph Lehrenfeld +1
We develop and analyze an embedded Trefftz-DG method for the steady incompressible Navier-Stokes equations, based on the reduced Oseen discretization from Part I. The main difficul…
Pressure-robustness for the axisymmetric Stokes problem by velocity reconstruction
Philip L. Lederer, Christoph Lehrenfeld, Christian Merdon +1
This paper studies pressure-robustness for the axisymmetric Stokes problem. The transformation to cylindrical coordinates requires that the radially weighted velocity is divergence…
High-order projection-based upwind method for simulation of transitional turbulent flows
Philip L. Lederer, Xaver Mooslechner, Joachim Schöberl
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) m…
Gradient-robust hybrid DG discretizations for the compressible Stokes equations
Philip L. Lederer, Christian Merdon
This paper studies two hybrid discontinuous Galerkin (HDG) discretizations for the velocity-density formulation of the compressible Stokes equations with respect to several desired…
Trefftz Discontinuous Galerkin discretization for the Stokes problem
Philip L. Lederer, Christoph Lehrenfeld, Paul Stocker
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 pointwis…
A discontinuous Galerkin approach for atmospheric flows with implicit condensation
Sabine Doppler, Philip L. Lederer, Joachim Schöberl +1
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…
High-order projection-based upwind method for implicit large eddy simulation
Philip L. Lederer, Xaver Mooslechner, Joachim Schöberl
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 cons…
A conforming auxiliary space preconditioner for the mass conserving mixed stress method
Lukas Kogler, Philip L. Lederer, Joachim Schöberl
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…
Analysis of Weakly Symmetric Mixed Finite Elements for Elasticity
Philip L. Lederer, Rolf Stenberg
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 give…
Mixed finite elements for Bingham flow in a pipe
Tom Gustafsson, Philip L. Lederer
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 base…
Hybridized Discontinuous Galerkin Methods for a Multiple Network Poroelasticity Model with Medical Applications
Johannes Kraus, Philip L. Lederer, Maria Lymbery +2
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, th…
A note on asymptotically exact a posteriori error estimates for mixed Laplace eigenvalue problems
Philip L. Lederer
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 literatur…
Divergence-conforming velocity and vorticity approximations for incompressible fluids obtained with minimal facet coupling
Jay Gopalakrishnan, Lukas Kogler, Philip L. Lederer +1
We introduce two new lowest order methods, a mixed method, and a hybrid Discontinuous Galerkin (HDG) method, for the approximation of incompressible flows. Both methods use diverge…
Energy norm analysis of exactly symmetric mixed finite elements for linear elasticity
Philip L. Lederer, Rolf Stenberg
We consider mixed finite element methods with exact symmetric stress tensors. We derive a new quasi-optimal a priori error estimate uniformly valid with respect to the compressibil…
Uniformly well-posed hybridized discontinuous Galerkin/hybrid mixed discretizations for Biot's consolidation model
Johannes Kraus, Philip L. Lederer, Maria Lymbery +1
We consider the quasi-static Biot's consolidation model in a three-field formulation with the three unknown physical quantities of interest being the displacement …
Guaranteed upper bounds for the velocity error of pressure-robust Stokes discretisations
Philip L. Lederer, Christian Merdon
This paper aims to improve guaranteed error control for the Stokes problem with a focus on pressure-robustness, i.e. for discretisations that compute a discrete velocity that is in…
A Hellan-Herrmann-Johnson-like method for the stream function formulation of the Stokes equations in two and three space dimensions
Philip L. Lederer
We introduce a new discretization for the stream function formulation of the incompressible Stokes equations in two and three space dimensions. The method is strongly related to th…
A pressure-robust embedded discontinuous Galerkin method for the Stokes problem by reconstruction operators
Philip L. Lederer, Sander Rhebergen
The embedded discontinuous Galerkin (EDG) finite element method for the Stokes problem results in a point-wise divergence-free approximate velocity on cells. However, the approxima…
Divergence-free tangential finite element methods for incompressible flows on surfaces
Philip L. Lederer, Christoph Lehrenfeld, Joachim Schöberl
In this work we consider the numerical solution of incompressible flows on two-dimensional manifolds. Whereas the compatibility demands of the velocity and the pressure spaces are…
A mass conserving mixed stress formulation for Stokes flow with weakly imposed stress symmetry
Jay Gopalakrishnan, Philip L. Lederer, Joachim Schöberl
We introduce a new discretization of a mixed formulation of the incompressible Stokes equations that includes symmetric viscous stresses. The method is built upon a mass conserving…
A mass conserving mixed stress formulation for the Stokes equations
Jay Gopalakrishnan, Philip L. Lederer, Joachim Schöberl
We propose a new discretization of a mixed stress formulation of the Stokes equations. The velocity is approximated with -conforming finite elements prov…
Hybrid Discontinuous Galerkin methods with relaxed H(div)-conformity for incompressible flows. Part II
Philip L. Lederer, Christoph Lehrenfeld, Joachim Schöberl
The present work is the second part of a pair of papers, considering Hybrid Discontinuous Galerkin methods with relaxed H(div)-conformity. The first part mainly dealt with presenti…
On reference solutions and the sensitivity of the 2D Kelvin-Helmholtz instability problem
Philipp W. Schroeder, Volker John, Philip L. Lederer +3
Two-dimensional Kelvin-Helmholtz instability problems are popular examples for assessing discretizations for incompressible flows at high Reynolds number. Unfortunately, the result…