107 citations · 459 across the 39 of their papers we have counts for
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An interface-tracking space-time hybridizable/embedded discontinuous Galerkin method for nonlinear free-surface flows
Giselle Sosa Jones, Sander Rhebergen
We present a compatible space-time hybridizable/embedded discontinuous Galerkin discretization for nonlinear free-surface waves. We pose this problem in a two-fluid (liquid and gas…
Convergence to weak solutions of a space-time hybridized discontinuous Galerkin method for the incompressible Navier--Stokes equations
Keegan L. A. Kirk, Ayçıl Çeşmelioǧlu, Sander Rhebergen
We prove that a space-time hybridized discontinuous Galerkin method for the evolutionary Navier--Stokes equations converges to a weak solution as the time step and mesh size tend t…
Analysis of pressure-robust embedded-hybridized discontinuous Galerkin methods for the Stokes problem under minimal regularity
Aaron Baier-Reinio, Sander Rhebergen, Garth N. Wells
We present analysis of two lowest-order hybridizable discontinuous Galerkin methods for the Stokes problem, while making only minimal regularity assumptions on the exact solution.…
A conforming sliding mesh technique for an embedded-hybridized discontinuous Galerkin discretization for fluid-rigid body interaction
Tamas L. Horvath, S. Rhebergen
In (J. Comput. Phys., 417, 109577, 2020) we introduced a space-time embedded-hybridizable discontinuous Galerkin method for the solution of the incompressible Navier-Stokes equatio…
Preconditioning for a pressure-robust HDG discretization of the Stokes equations
Sander Rhebergen, Garth N. Wells
We introduce a new preconditioner for a recently developed pressure-robust hybridized discontinuous Galerkin (HDG) finite element discretization of the Stokes equations. A feature…
Analysis of an exactly mass conserving space-time hybridized discontinuous Galerkin method for the time-dependent Navier--Stokes equations
Keegan L. A. Kirk, Tamás L. Horváth, Sander Rhebergen
We introduce and analyze a space-time hybridized discontinuous Galerkin method for the evolutionary Navier--Stokes equations. Key features of the numerical scheme include point-wis…