14 citations · 17 across the 7 of their papers we have counts for
7 papers
Local error estimates for a finite element method combining linear and nonlinear stabilization for the linear hyperbolic transport equation
Erik Burman, Fabian Heimann
In this paper, we investigate the combination of a linear continuous interior penalty type and a non-linear artificial diffusion stabilisation applied to the transport problem, bas…
Higher Order Unfitted Space-Time Methods for Transport Problems
Erik Burman, Fabian Heimann
In this article, we present an Unfitted Space-Time Finite Element method for the scalar transport equation posed on moving domains. We consider the case of the domain boundary bein…
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…
A Higher Order Unfitted Space-Time Finite Element Method for Coupled Surface-Bulk problems
Fabian Heimann
We present a higher order space-time unfitted finite element method for convection-diffusion problems on coupled (surface and bulk) domains. In that way, we combine a method sugges…
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…
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…
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…