10 papers
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…
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…
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…
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…
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…