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In the present work, we examine and analyze an hp-version interior penalty discontinuous Galerkin finite element method for the numerical approximation of a steady fluid system on computational meshes consisting of polytopic elements on the…

Numerical Analysis · Mathematics 2024-04-26 Efthymios N. Karatzas

We propose a mixed finite element method for the motion of a strongly viscous, ideal, and isentropic gas. At the boundary we impose a Navier-slip condition such that the velocity equation can be posed in mixed form with the vorticity as an…

Numerical Analysis · Mathematics 2009-11-11 Kenneth Karlsen , Trygve Karper

We investigate a numerical behaviour of robust deterministic optimal control problem subject to a convection diffusion equation containing uncertain inputs. Stochastic Galerkin approach, turning the original optimization problem containing…

Numerical Analysis · Mathematics 2023-03-01 Pelin Çiloğlu , Hamdullah Yücel

A new discontinuous Galerkin finite element method for the Stokes equations is developed in the primary velocity-pressure formulation. This method employs discontinuous polynomials for both velocity and pressure on general…

Numerical Analysis · Mathematics 2021-05-05 Xiu Ye , Shangyou Zhang

This work presents a novel stabilization strategy for the Galerkin formulation of the incompressible Navier-Stokes equations, developed to achieve high accuracy while ensuring convergence and compatibility with high-order elements on…

Numerical Analysis · Mathematics 2025-09-05 Antonio Blanco-Casares , Vishal Kumar , Daniel Mira , Oriol Lehmkuhl

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) domain and use a time-dependent level-set function to…

Numerical Analysis · Mathematics 2023-07-10 Giselle Sosa Jones , Sander Rhebergen

We study the weak Galerkin finite element method for Stokes problem. A new weak Galerkin finite element velocity-pressure space pair is presented which satisfies the discrete inf-sup condition. Based on this space pair, we establish a…

Numerical Analysis · Mathematics 2018-01-30 Tie Zhang , Tao Lin

Divergence-free discontinuous Galerkin (DG) finite element methods offer a suitable discretization for the pointwise divergence-free numerical solution of Borrvall and Petersson's model for the topology optimization of fluids in Stokes flow…

Numerical Analysis · Mathematics 2022-02-22 Ioannis P. A. Papadopoulos

In this paper we propose a new spatially high order accurate semi-implicit discontinuous Galerkin (DG) method for the solution of the two dimensional incompressible Navier-Stokes equations on staggered unstructured curved meshes. While the…

Numerical Analysis · Mathematics 2014-07-07 Maurizio Tavelli , Michael Dumbser

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

Provable stable arbitrary order symmetric interior penalty discontinuous Galerkin (SIP) discretisations of variable viscosity, incompressible Stokes flow utilising $Q^2_k$--$Q_{k-1}$ elements and hierarchical Legendre basis polynomials are…

Numerical Analysis · Mathematics 2017-03-07 Dominic E. Charrier , Dave A. May , Sascha M. Schnepp

We present an efficient nodal discontinuous Galerkin method for approximating nearly incompressible flows using the Boltzmann equations. The equations are discretized with Hermite polynomials in velocity space yielding a first order…

Numerical Analysis · Mathematics 2019-05-22 A. Karakus , N. Chalmers , J. S. Hesthaven , T. Warburton

Grad-div stabilization is a classical remedy in conforming mixed finite element methods for incompressible flow problems, for mitigating velocity errors that are sometimes called poor mass conservation. Such errors arise due to the…

Numerical Analysis · Mathematics 2019-04-12 Mine Akbas , Alexander Linke , Leo G. Rebholz , Philipp W. Schroeder

We consider a stabilization method for divergence-conforming B-spline discretizations of the incompressible Navier--Stokes problem wherein jumps in high-order normal derivatives of the velocity field are penalized across interior mesh…

Numerical Analysis · Mathematics 2022-01-28 Guoxiang Grayson Tong , David Kamensky , John A. Evans

This work uses high-order discontinuous Galerkin discretization techniques as a generic, parameter-free, and reliable tool to accurately predict transitional and turbulent flows through medical devices. Flows through medical devices are…

Fluid Dynamics · Physics 2018-11-19 Niklas Fehn , Wolfgang A. Wall , Martin Kronbichler

Finite element discretization of Stokes problems can result in singular, inconsistent saddle point linear algebraic systems. This inconsistency can cause many iterative methods to fail to converge. In this work, we consider the lowest-order…

Numerical Analysis · Mathematics 2024-12-16 Weizhang Huang , Zhuoran Wang

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

Using the T-coercivity theory as advocated in [Chesnel, Ciarlet, T -coercivity and continuous Galerkin methods: application to transmission problems with sign changing coefficients (2013)], we propose a new variational formulation of the…

Numerical Analysis · Mathematics 2024-10-21 Patrick Ciarlet , Erell Jamelot

The present paper addresses the numerical solution of turbulent flows with high-order discontinuous Galerkin methods for discretizing the incompressible Navier-Stokes equations. The efficiency of high-order methods when applied to…

Fluid Dynamics · Physics 2018-08-29 Niklas Fehn , Wolfgang A. Wall , Martin Kronbichler

We develop a family of $H(\mathrm{div})$-conforming hybridizable discontinuous Galerkin methods for the steady Stokes equations based on BDM and RT velocity spaces with either discontinuous or continuous hybrid traces. In contrast to our…

Numerical Analysis · Mathematics 2026-04-23 Gang Chen , Wenyi Liu , Yangwen Zhang