English
Related papers

Related papers: A simple preconditioner for a discontinuous Galerk…

200 papers

Solving the Stokes equation by an optimal domain decomposition method derived algebraically involves the use of non standard interface conditions whose discretisation is not trivial. For this reason the use of approximation methods such as…

Numerical Analysis · Mathematics 2019-10-02 Gabriel R. Barrenechea , Michał Bosy , Victorita Dolean , Frédéric Nataf , Pierre-Henri Tournier

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. The methods under consideration have previously been shown…

Numerical Analysis · Mathematics 2023-07-07 Aaron Baier-Reinio , Sander Rhebergen , Garth N. Wells

We present optimal preconditioners for a recently introduced hybridized discontinuous Galerkin finite element discretization of the Stokes equations. Typical of hybridized discontinuous Galerkin methods, the method has degrees-of-freedom…

Numerical Analysis · Mathematics 2023-07-06 Sander Rhebergen , Garth N. Wells

We propose a new discretization method for the Stokes equations. The method is an improved version of the method recently presented in [C. Lehrenfeld, J. Sch\"oberl, Comp. Meth. Appl. Mech. Eng., 361 (2016)] which is based on an…

Numerical Analysis · Mathematics 2018-03-29 Philip L. Lederer , Christoph Lehrenfeld , Joachim Schöberl

We present an optimal preconditioner for the exactly divergence-free discontinuous Galerkin (DG) discretization of Cockburn, Kanschat, and Sch\"otzau [J. Sci. Comput., 31 (2007), pp. 61--73] and Wang and Ye [SIAM J. Numer. Anal., 45 (2007),…

Numerical Analysis · Mathematics 2022-03-29 Sander Rhebergen , Ben S. Southworth

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

A discontinuous Galerkin method by patch reconstruction is proposed for Stokes flows. A locally divergence-free reconstruction space is employed as the approximation space, and the interior penalty method is adopted which imposes the normal…

Numerical Analysis · Mathematics 2019-11-26 Ruo Li , Zhiyuan Sun , Zhijian Yang

We present and analyze a new embedded--hybridized discontinuous Galerkin finite element method for the Stokes problem. The method has the attractive properties of full hybridized methods, namely an $H({\rm div})$-conforming velocity field,…

Numerical Analysis · Mathematics 2023-07-06 Sander Rhebergen , Garth N. Wells

We introduce a hybridizable discontinuous Galerkin method for the incompressible Navier--Stokes equations for which the approximate velocity field is pointwise divergence-free. The method builds on the method presented by Labeur and Wells…

Numerical Analysis · Mathematics 2023-07-04 Sander Rhebergen , Garth N. Wells

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

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

In this paper we propose a pressure robust staggered discontinuous Galerkin method for the Stokes equations on general polygonal meshes by using piecewise constant approximations. We modify the right hand side of the body force in the…

Numerical Analysis · Mathematics 2020-07-02 Lina Zhao , Eun-Jae Park , Eric Chung

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

In this paper, we present a divergence-conforming discontinuous Galerkin finite element method for Stokes eigenvalue problems. We prove a priori error estimates for the eigenvalue and eigenfunction errors and present a robust residual based…

Numerical Analysis · Mathematics 2018-05-24 Joscha Gedicke , Arbaz Khan

We present and analyze a hybridizable discontinuous Galerkin (HDG) finite element method for the coupled Stokes--Biot problem. Of particular interest is that the discrete velocities and displacement are $H(\text{div})$-conforming and…

Numerical Analysis · Mathematics 2023-07-07 Aycil Cesmelioglu , Jeonghun J. Lee , Sander Rhebergen

We propose parameter-robust preconditioners for the statically condensed linear system arising from a hybridizable discontinuous Galerkin discretization of the coupled Stokes--Darcy system. The design strategy relies on first applying the…

Numerical Analysis · Mathematics 2026-04-27 Esteban Henríquez , Miroslav Kuchta , Jeonghun J. Lee , Sander Rhebergen

In this work we consider a discontinuous Galerkin method for the discretization of the Stokes problem. We use $H(\textrm{div})$-conforming finite elements as they provide major benefits such as exact mass conservation and…

Numerical Analysis · Mathematics 2016-12-06 Philip L. Lederer , Joachim Schöberl

This paper proposes a novel computational framework for the solution of geometrically parametrised flow problems governed by the Stokes equation. The proposed method uses a high-order hybridisable discontinuous Galerkin formulation and the…

Numerical Analysis · Mathematics 2020-09-10 Ruben Sevilla , Luca Borchini , Matteo Giacomini , Antonio Huerta

We present a high-order hybridized discontinuous Galerkin (HDG) method for the fully coupled time-dependent Stokes-Darcy-transport problem where the fluid viscosity and source/sink terms depend on the concentration and the…

Numerical Analysis · Mathematics 2023-07-07 Aycil Cesmelioglu , Dinh Dong Pham , 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
‹ Prev 1 2 3 10 Next ›