相关论文: A uniform and pressure-robust enriched Galerkin me…
In this paper, we present a pressure-robust enriched Galerkin (EG) scheme for solving the Stokes equations, which is an enhanced version of the EG scheme for the Stokes problem proposed in [Son-Young Yi, Xiaozhe Hu, Sanghyun Lee, James H.…
In this paper, we develop a novel enriched Galerkin (EG) method for the steady incompressible Navier-Stokes equations in rotational form, which is both pressure-robust and parameter-free. The EG space employed here, originally proposed in…
We present a new enriched Galerkin (EG) scheme for the Stokes equations based on piecewise linear elements for the velocity unknowns and piecewise constant elements for the pressure. The proposed EG method augments the conforming piecewise…
In this paper, we propose a low-cost, parameter-free, and pressure-robust Stokes solver based on the enriched Galerkin (EG) method with a discontinuous velocity enrichment function. The EG method employs the interior penalty discontinuous…
We propose a pressure-robust enriched Galerkin (EG) finite element method for the incompressible Navier-Stokes and heat equations in the Boussinesq regime. For the Navier-Stokes equations, the EG formulation combines continuous Lagrange…
This paper presents an enriched Galerkin (EG) finite element method for the incompressible Navier--Stokes equations. The method augments continuous piecewise linear velocity spaces with elementwise bubble functions, yielding a locally…
The embedded discontinuous Galerkin (EDG) finite element method for the Stokes problem results in a point-wise divergence-free approximate velocity on cells. However, the approximate velocity is not H(div)-conforming and it can be shown…
This paper presents a novel Stabilizer-Free weak Galerkin (WG) finite element method for solving the Brinkman equations without the need for conventional stabilization techniques. The Brinkman model, which mathematically blends features of…
The Brinkman equations can be regarded as a combination of the Stokes and Darcy equations which model transitions between the fast flow in channels (governed by Stokes equations) and the slow flow in porous media (governed by Darcy's law).…
We propose a novel parameter-free and locking-free enriched Galerkin (EG) method for solving the linear elasticity problem in both two and three dimensions. Unlike existing locking-free EG methods, our method enriches the first-order…
In this paper, we develop an arbitrary-order locking-free enriched Galerkin method for the linear elasticity problem using the stress-displacement formulation in both two and three dimensions. The method is based on the mixed discontinuous…
In this paper, we propose a pressure-robust weak Galerkin (WG) finite element scheme to solve the Stokes-Darcy problem. To construct the pressure-robust numerical scheme, we use the divergence-free velocity reconstruction operator to modify…
In this paper we propose a novel staggered discontinuous Galerkin method for the Brinkman problem on general quadrilateral and polygonal meshes. The proposed method is robust in the Stokes and Darcy limits, in addition, hanging nodes can be…
In this work we present an enriched Petrov-Galerkin (EPG) method for the simulation of the Darcy flow in porous media. The new method enriches the approximation trial space of the conforming continuous Galerkin (CG) method with bubble…
This paper introduces a novel weak Galerkin (WG) finite element method for the numerical solution of the Brinkman equations. The Brinkman model, which seamlessly integrates characteristics of both the Stokes and Darcy equations, is employed…
In this paper, we propose an enriched Galerkin (EG) approximation for a two-phase pressure saturation system with capillary pressure in heterogeneous porous media. The EG methods are locally conservative, have fewer degrees of freedom…
This paper presents a stable numerical algorithm for the Brinkman equations by using weak Galerkin (WG) finite element methods. The Brinkman equations can be viewed mathematically as a combination of the Stokes and Darcy equations which…
We develop an enriched Galerkin (EG) method for the incompressible Navier-Stokes equations that conserves both kinetic energy and helicity in the inviscid limit without introducing any additional projection variables. The method employs an…
Accurate simulation of the coupled fluid flow and solid deformation in porous media is challenging, especially when the media permeability and storativity are heterogeneous. We apply the enriched Galerkin (EG) finite element method for the…
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…