5 papers · 1 filter
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…
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…
Inverse obstacle scattering regularized by the tangent-point energy
Henrik Schumacher, Jannik Rönsch, Thorsten Hohage +1
We employ the so-called tangent-point energy as Tikhonov regularizer for ill-conditioned inverse scattering problems in 3D. The tangent-point energy is a self-avoiding functional o…
On the improved convergence of lifted distributional Gauss curvature from Regge elements
Jay Gopalakrishnan, Michael Neunteufel, Joachim Schöberl +1
Although Regge finite element functions are not continuous, useful generalizations of nonlinear derivatives like the curvature, can be defined using them. This paper is devoted to…
Generalizing Riemann curvature to Regge metrics
Jay Gopalakrishnan, Michael Neunteufel, Joachim Schöberl +1
In this paper, we propose a generalization of the Riemann curvature tensor on manifolds (of dimension two or higher) endowed with a Regge metric. Specifically, while all components…