Related papers: Weak Galerkin Methods for the Brinkman Equations
From the steady Stokes and Navier-Stokes models, a penalization method has been considered by several authors for approximating those fluid equations around obstacles. In this work, we present a justification for using fictitious domains to…
This paper introduces an efficient stabilizer-free weak Galerkin (WG) finite element method for solving the three-dimensional quad-curl problem. Leveraging bubble functions as a key analytical tool, the method extends the applicability of…
We consider the dynamic Biot model (see [Biot, M. A. J. Appl. Phys. 33, 1482--1498 (1962)]) describing the interaction between fluid flow and solid deformation including wave propagation phenomena in both the liquid and solid phases of a…
The development and application of the Discontinuous Galerkin (DG) method have attracted great attention in computational fluid dynamics (CFD) com- munity in the past decades. The underlying reason for such an intensive investigation is due…
The moving discontinuous Galerkin finite element method with interface condition enforcement (MDG-ICE) is applied to the case of viscous flows. This method uses a weak formulation that separately enforces the conservation law, constitutive…
We consider the generalized Forchheimer flows for slightly compressible fluids. Using Muskat's and Ward's general form of Forchheimer equations, we describe the fluid dynamics by a nonlinear degenerate parabolic equation for the density. We…
This paper presents a numerical approximation technique for the Boltzmann equation based on a moment system approximation in velocity dependence and a discontinuous Galerkin finite-element approximation in position dependence. The closure…
We propose an efficient threshold dynamics method for topology optimization for fluids modeled with the Stokes equation. The proposed algorithm is based on minimization of an objective energy function that consists of the dissipation power…
In this paper, we develop and analyze a novel numerical scheme for the steady incompressible Navier-Stokes equations by the weak Galerkin methods. The divergence-preserving velocity reconstruction operator is employed in the discretization…
We propose a linearized semi-implicit and decoupled finite element method for the incompressible Navier--Stokes equations with variable density. Our method is fully discrete and shown to be unconditionally stable. The velocity equation is…
This paper presents a rigorous finite element framework for solving an optimal control problem governed by the steady Navier-Stokes-Brinkman equations, focusing on identifying a scalar permeability parameter $\gamma$ from local velocity…
The discontinuous Galerkin (DG) method is an established method for computing approximate solutions of partial differential equations in many applications. Unlike continuous finite elements, in DG methods, numerical fluxes are used to…
This article concerns the weak Galerkin mixed finite element method (WG-MFEM) for second order elliptic equations on 2D domains with curved boundary. The Neumann boundary condition is considered since it becomes the essential boundary…
The goal of this article is to clarify some misunderstandings and inappropriate claims made in [6] regarding the relation between the weak Galerkin (WG) finite element method and the hybridizable discontinuous Galerkin (HDG). In this paper,…
In this paper, we first introduce an abstract framework to solve the eigenvalue problem by weak Galerkin (WG) method. By the application of the framework, WG method is proved to be locking-free and gives asymptotic lower bounds for the…
This article proposes a novel least-squares weak Galerkin (LS-WG) method for second-order elliptic equations in non-divergence form. The approach leverages a locally defined discrete weak Hessian operator constructed within the weak…
In this paper, we rewrite the Stokes eigenvalue problem as an Elliptic eigenvalue problem restricted to subspace, and introduce an abstract framework of solving abstract elliptic eigenvalue problem to give the WG scheme, error estimates and…
A weak Galerkin (WG) finite element method without stabilizers was introduced in [J. Comput. Appl. Math., 371 (2020). arXiv:1906.06634] on polytopal mesh. Then it was improved in [arXiv:2008.13631] with order one superconvergence. The goal…
We introduce a very weak space-time variational formulation for the wave equation, prove its well-posedness (even in the case of minimal regularity) and optimal inf-sup stability. Then, we introduce a tensor product-style space-time…
We present projection-based mixed finite element methods for the solution of the unsteady Brinkman equations for incompressible single-phase flow with fixed in space porous solid inclusions. At each time step the method requires the…