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A scheme for the solution of fluid-structure interaction (FSI) problems with weakly compressible flows is proposed in this work. A novel hybridizable discontinuous Galerkin (HDG) method is derived for the discretization of the fluid…

This paper presents a high-order discontinuous Galerkin finite element method to solve the barotropic version of the conservative symmetric hyperbolic and thermodynamically compatible (SHTC) model of compressible two-phase flow, introduced…

Numerical Analysis · Mathematics 2025-01-29 Laura Río-Martín , Michael Dumbser

The present work focuses on the geometric parametrization and the reduced order modeling of the Stokes equation. We discuss the concept of a parametrized geometry and its application within a reduced order modeling technique. The full order…

Numerical Analysis · Mathematics 2021-06-01 Nirav Vasant Shah , Martin Hess , Gianluigi Rozza

We present a robust and accurate discretization approach for incompressible turbulent flows based on high-order discontinuous Galerkin methods. The DG discretization of the incompressible Navier-Stokes equations uses the local…

Fluid Dynamics · Physics 2018-08-01 Niklas Fehn , Wolfgang A Wall , Martin Kronbichler

The present paper deals with the numerical solution of the incompressible Navier-Stokes equations using high-order discontinuous Galerkin (DG) methods for discretization in space. For DG methods applied to the dual splitting projection…

Numerical Analysis · Mathematics 2017-10-25 Niklas Fehn , Wolfgang A. Wall , Martin Kronbichler

The Isogeometric Analysis (IgA) of boundary value problems in complex domains often requires a decomposition of the computational domain into patches such that each of which can be parametrized by the so-called geometrical mapping. In this…

Numerical Analysis · Mathematics 2016-10-13 Christoph Hofer , Ulrich Langer , Ioannis Toulopoulos

In this paper we present an efficient discretization method for the solution of the unsteady incompressible Navier-Stokes equations based on a high order (Hybrid) Discontinuous Galerkin formulation. The crucial component for the efficiency…

Numerical Analysis · Mathematics 2016-06-29 Christoph Lehrenfeld , Joachim Schöberl

We study the numerical approximation of a coupled hyperbolic-parabolic system by a family of discontinuous Galerkin space-time finite element methods. The model is rewritten as a first-order evolutionary problem that is treated by the…

Numerical Analysis · Mathematics 2024-06-21 Markus Bause , Sebastian Franz

We propose and analyze discontinuous Galerkin (dG) approximations to 3D-1D coupled systems which model diffusion in a 3D domain containing a small inclusion reduced to its 1D centerline. Convergence to weak solutions of a steady state…

Numerical Analysis · Mathematics 2023-12-29 Rami Masri , Miroslav Kuchta , Beatrice Riviere

In this paper we consider discontinuous Galerkin (DG) methods for the incompressible Navier-Stokes equations in the framework of projection methods. In particular we employ symmetric interior penalty DG methods within the second-order…

Numerical Analysis · Mathematics 2017-11-27 Marian Piatkowski , Steffen Müthing , Peter Bastian

In this paper we consider a conservative discretization of the two-dimensional incompressible Navier--Stokes equations. We propose an extension of Arakawa's classical finite difference scheme for fluid flow in the vorticity-stream function…

Computational Physics · Physics 2017-01-06 Lukas Einkemmer , Matthias Wiesenberger

In this paper we establish best approximation type error estimates for the fully discrete Galerkin solutions of the time-dependent Stokes problem using the stream-function formulation. For the time discretization we use the discontinuous…

Numerical Analysis · Mathematics 2026-05-20 Dmitriy Leykekhman , Boris Vexler , Jakob Wagner

This work aims at presenting a Discontinuous Galerkin (DG) formulation employing a spectral basis for two important models employed in cardiac electrophysiology, namely the monodomain and bidomain models. The use of DG methods is motivated…

Numerical Analysis · Mathematics 2025-03-24 Federica Botta , Matteo Calafà , Pasquale C. Africa , Christian Vergara , Paola F. Antonietti

We present a high-order entropy stable discontinuous Galerkin (ESDG) method for nonlinear conservation laws on both multi-dimensional domains and on networks constructed from one-dimensional domains. These methods utilize treatments of…

Numerical Analysis · Mathematics 2021-07-23 Xinhui Wu , Jesse Chan

The high-order accurate continuous Galerkin finite element method offers attractive computational efficiency for computational fluid dynamics. A challenge is however spurious oscillations which result for convection dominated flows over…

Numerical Analysis · Mathematics 2023-11-10 Arnaud G. Malan , Jan Nordstrom

In this paper we propose a novel arbitrary high order accurate semi-implicit space-time discontinuous Galerkin method for the solution of the two dimensional incompressible Navier-Stokes equations on staggered unstructured triangular…

Numerical Analysis · Mathematics 2014-12-04 Maurizio Tavelli , Michael Dumbser

We apply geometric multigrid methods for the finite element approximation of flow problems governed by Darcy and Brinkman systems used in modeling highly heterogeneous porous media. The method is based on divergence-conforming discontinuous…

Numerical Analysis · Mathematics 2021-02-02 Guido Kanschat , Raytcho Lazarov , Youli Mao

A multigrid method for the Stokes system discretized with an Hdiv-conforming discontinuous Galerkin method is presented. It acts on the combined velocity and pressure spaces and thus does not need a Schur complement approximation. The…

Numerical Analysis · Mathematics 2016-02-22 Guido Kanschat , Youli Mao

Stability and error analysis of a hybridized discontinuous Galerkin finite element method for Stokes equations is presented. The method is locally conservative, and for particular choices of spaces the velocity field is point-wise…

Numerical Analysis · Mathematics 2018-02-01 Sander Rhebergen , Garth N. Wells

A novel numerical approach to solving the shallow-water equations on the sphere using high-order numerical discretizations in both space and time is proposed. A space-time tensor formalism is used to express the equations of motion…

Numerical Analysis · Mathematics 2021-11-12 Stéphane Gaudreault , Martin Charron , Valentin Dallerit , Mayya Tokman