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Related papers: A Pressure-Robust Weak Galerkin Finite Element Met…

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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

In this paper, we propose a new stabilizer free and pressure robust WG method for the Stokes equations with super-convergence on polytopal mesh in the primary velocity-pressure formulation. Convergence rates with one order higher than the…

Numerical Analysis · Mathematics 2020-11-04 Lin Mu , Xiu Ye , Shangyou Zhang

We present and analyze a strongly conservative hybridizable discontinuous Galerkin finite element method for the coupled incompressible Navier-Stokes and Darcy problem with Beavers-Joseph-Saffman interface condition. An a priori error…

Numerical Analysis · Mathematics 2023-07-07 Aycil Cesmelioglu , Sander Rhebergen

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

We present a Lagrange--Galerkin scheme free from numerical quadrature for the Navier--Stokes equations. Our idea is to use a locally linearized velocity and the backward Euler method in finding the position of fluid particle at the previous…

Numerical Analysis · Mathematics 2015-05-26 Masahisa Tabata , Shinya Uchiumi

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

A newly developed weak Galerkin method is proposed to solve parabolic equations. This method allows the usage of totally discontinuous functions in approximation space and preserves the energy conservation law. Both continuous and…

Numerical Analysis · Mathematics 2013-03-18 Qiaoluan H. Li , Junping Wang

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

This paper applies a discontinuous Galerkin finite element method to the Kelvin-Voigt viscoelastic fluid motion equations when the forcing function is in $L^\infty({\bf L}^2)$-space. Optimal a priori error estimates in $L^\infty({\bf…

Numerical Analysis · Mathematics 2022-02-10 Saumya Bajpai , Deepjyoti Goswami , Kallol Ray

In a recent work [10], we have introduced a pressure-robust Hybrid High-Order method for the numerical solution of the incompressible Navier-Stokes equations on matching simplicial meshes. Pressure-robust methods are characterized by error…

Numerical Analysis · Mathematics 2026-01-22 Daniel Castanon Quiroz , Daniele A. Di Pietro

Based on a discontinuous Galerkin method in the spatial directions and an improved implicit-explicit pressure-correction scheme in the temporal direction, this paper discusses a fully discrete scheme for the…

Numerical Analysis · Mathematics 2026-05-01 Bikram Bir , Amiya K. Pani

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

This paper develops and analyzes a class of semi-discrete and fully discrete weak Galerkin finite element methods for unsteady incompressible convective Brinkman-Forchheimer equations. For the spatial discretization, the methods adopt the…

Numerical Analysis · Mathematics 2024-10-30 Xiaojuan Wang , Jihong Xiao , Xiaoping Xie , Shiquan Zhang

Combining the characteristic method and the local discontinuous Galerkin method with carefully constructing numerical fluxes, we design the variational formulations for the time-dependent convection-dominated Navier-Stokes equations in…

Computational Physics · Physics 2017-04-03 Shuqin Wang , Weihua Deng , Yujiang Wu , Jinyun Yuan

This article focusses on the analysis of a conforming finite element method for the time-dependent incompressible Navier-Stokes equations. For divergence-free approximations, in a semi-discrete formulation, we prove error estimates for the…

Numerical Analysis · Mathematics 2018-03-20 Philipp W. Schroeder , Gert Lube

We study the steady-state Navier-Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion. For…

Numerical Analysis · Mathematics 2016-04-26 Bedřich Sousedík , Howard C. Elman

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

A new high order accurate staggered semi-implicit space-time discontinuous Galerkin (DG) method is presented for the simulation of viscous incompressible flows on unstructured triangular grids in two space dimensions. The staggered DG…

Numerical Analysis · Mathematics 2020-10-09 Francesco Lohengrin Romeo , Michael Dumbser , Maurizio Tavelli

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

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