211 citations · 712 across the 40 of their papers we have counts for
47 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…
Releasing the pressure: High-order surface flow discretizations via discrete Helmholtz-Hodge decompositions
Tim Brüers, Christoph Lehrenfeld, Tim van Beeck +1
We present a discrete Helmholtz--Hodge decomposition for H(div)-conforming Brezzi--Douglas--Marini (BDM) finite elements on triangulated surfaces of arbitrary topology. The diverge…
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…
Streamfunction-vorticity formulation for incompressible viscid and inviscid flows on general surfaces
Tim Brüers, Christoph Lehrenfeld, Max Wardetzky
This paper presents a streamfunction-vorticity formulation for the Navier--Stokes and Euler equations on general surfaces. Notably, this includes non-simply connected surfaces, on…
Hybrid discontinuous Galerkin discretizations for the damped time-harmonic Galbrun's equation
Martin Halla, Christoph Lehrenfeld, Tim van Beeck
In this article, we study the damped time-harmonic Galbrun's equation which models solar and stellar oscillations. We introduce and analyze hybrid discontinuous Galerkin discretiza…
Discretization Error Analysis of a High Order Unfitted Space-Time Method for moving domain problems
Fabian Heimann, Christoph Lehrenfeld, Janosch Preuß
We present a numerical analysis of a higher order unfitted space-time Finite Element method applied to a convection-diffusion model problem posed on a moving bulk domain. The metho…
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…
Sparsity comparison of polytopal finite element methods
Christoph Lehrenfeld, Paul Stocker, Maximilian Zienecker
In this work we compare crucial parameters for efficiency of different finite element methods for solving partial differential equations (PDEs) on polytopal meshes. We consider the…
LiveDocs: Crafting Interactive Development Environments From Research Findings
Pedro Costa Klein, Christoph Lehrenfeld, Markus Osterhoff +1
Open Science is a recurrent topic in scientific discussion, and there is a current effort to make research more accessible to a broader audience. A focus on delivering research fin…
Geometry Error Analysis of a parametric mapping for Higher Order Unfitted Space-Time Methods
Fabian Heimann, Christoph Lehrenfeld
In [Heimann, Lehrenfeld, Preuß, SIAM J. Sci. Comp. 45(2), 2023, B139 - B165] new geometrically unfitted space-time Finite Element methods for partial differential equations posed o…
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…
Analysis of divergence-preserving unfitted finite element methods for the mixed Poisson problem
Christoph Lehrenfeld, Tim van Beeck, Igor Voulis
In this paper we present a new H(div)-conforming unfitted finite element method for the mixed Poisson problem which is robust in the cut configuration and preserves conservation pr…
Unfitted Trefftz discontinuous Galerkin methods for elliptic boundary value problems
Fabian Heimann, Christoph Lehrenfeld, Paul Stocker +1
We propose a new geometrically unfitted finite element method based on discontinuous Trefftz ansatz spaces. Trefftz methods allow for a reduction in the number of degrees of freedo…
Research-Data Management Planning in the German Mathematical Community
Tobias Boege, René Fritze, Christiane Görgen +13
In this paper we discuss the notion of research data for the field of mathematics and report on the status quo of research-data management and planning. A number of decentralized a…
A new T-compatibility condition and its application to the discretization of the damped time-harmonic Galbrun's equation
Martin Halla, Christoph Lehrenfeld, Paul Stocker
We consider the approximation of weakly T-coercive operators. The main property to ensure the convergence thereof is the regularity of the approximation (in the vocabulary of discr…
Robust finite element discretizations for a simplified Galbrun's equation
Tilman Alemán, Martin Halla, Christoph Lehrenfeld +1
Driven by the challenging task of finding robust discretization methods for Galbrun's equation, we investigate conditions for stability and different aspects of robustness for diff…
Geometrically Higher Order Unfitted Space-Time Methods for PDEs on Moving Domains
Fabian Heimann, Christoph Lehrenfeld, Janosch Preuß
In this paper, we propose new geometrically unfitted space-time Finite Element methods for partial differential equations posed on moving domains of higher order accuracy in space…
Embedded Trefftz discontinuous Galerkin methods
Christoph Lehrenfeld, Paul Stocker
In Trefftz discontinuous Galerkin methods a partial differential equation is discretized using discontinuous shape functions that are chosen to be elementwise in the kernel of the…
Isoparametric unfitted BDF -- Finite element method for PDEs on evolving domains
Yimin Lou, Christoph Lehrenfeld
We propose a new discretization method for PDEs on moving domains in the setting of unfitted finite element methods, which is provably higher-order accurate in space and time. In t…
Learned infinite elements
Thorsten Hohage, Christoph Lehrenfeld, Janosch Preuss
We study the numerical solution of scalar time-harmonic wave equations on unbounded domains which can be split into a bounded interior domain of primary interest and an exterior do…
An unfitted Eulerian finite element method for the time-dependent Stokes problem on moving domains
Henry von Wahl, Thomas Richter, Christoph Lehrenfeld
We analyse a Eulerian Finite Element method, combining a Eulerian time-stepping scheme applied to the time-dependent Stokes equations using the CutFEM approach with inf-sup stable…
Sweeping preconditioners for stratified media in the presence of reflections
Janosch Preuß, Thorsten Hohage, Christoph Lehrenfeld
In this paper we consider sweeping preconditioners for time harmonic wave propagation in stratified media, especially in the presence of reflections. In the most famous class of sw…
Locking free and gradient robust H(div)-conforming HDG methods for linear elasticity
Guosheng Fu, Christoph Lehrenfeld, Alexander Linke +1
Robust discretization methods for (nearly-incompressible) linear elasticity are free of volume-locking and gradient-robust. While volume-locking is a well-known problem that can be…