Related papers: A Weak Galerkin Mixed Finite Element Method for Se…
This paper proposes and analyzes a class of new weak Galerkin (WG) finite element methods for 2- and 3-dimensional linear elasticity problems. The methods use discontinuous piecewise-polynomial approximations of degrees $k(\geq 0)$ for the…
In this paper, we propose a simple numerical algorithm based on the weak Galerkin (WG) finite element method for a class of fourth-order problems in fluorescence tomography (FT), eliminating the need for stabilizer terms required in…
In this paper, we introduce and analyze a lowest-order locking-free weak Galerkin (WG) finite element scheme for the grad-div formulation of linear elasticity problems. The scheme uses linear functions in the interior of mesh elements and…
This paper introduces new discretization schemes for time-harmonic Maxwell equations in a connected domain by using the weak Galerkin (WG) finite element method. The corresponding WG algorithms are analyzed for their stability and…
In this paper, we propose a weak Galerkin (WG) finite element method for the Maxwell eigenvalue problem. By restricting subspaces, we transform the mixed form of Maxwell eigenvalue problem into simple elliptic equation. Then we give the WG…
A new primal-dual weak Galerkin (PDWG) finite element method is introduced and analyzed for the ill-posed elliptic Cauchy problems with ultra-low regularity assumptions on the exact solution. The Euler-Lagrange formulation resulting from…
This paper presents a generalized weak Galerkin (gWG) finite element method for linear elasticity problems on general polygonal and polyhedral meshes. The proposed framework is flexible and efficient, allowing for the use of nonpolynomial…
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…
The embedded discontinuous Galerkin (EDG) method by Cockburn et al. [SIAM J. Numer. Anal., 2009, 47(4), 2686-2707] is obtained from the hybridizable discontinuous Galerkin method by changing the space of the Lagrangian multiplier from…
In this work, the authors introduce a generalized weak Galerkin (gWG) finite element method for the time-dependent Oseen equation. The generalized weak Galerkin method is based on a new framework for approximating the gradient operator.…
We consider the singularly perturbed fourth-order boundary value problem $\varepsilon ^{2}\Delta ^{2}u-\Delta u=f $ on the unit square $\Omega \subset \mathbb{R}^2$, with boundary conditions $u = \partial u / \partial n = 0$ on $\partial…
A stabilizer free weak Galerkin (WG) finite element method on polytopal mesh has been introduced in Part I of this paper (J. Comput. Appl. Math, 371 (2020) 112699. arXiv:1906.06634.) Removing stabilizers from discontinuous finite element…
In this article, a weak Galerkin method is firstly presented and analyzed for the quasi-linear elliptic problem of non-monotone type. By using Brouwer's fixed point technique, the existence of WG solution and error estimates in both the…
Recently, a new stabilizer free weak Galerkin method (SFWG) is proposed, which is easier to implement and more efficient. The main idea is that by letting $j\geq j_{0}$ for some $j_{0}$, where $j$ is the degree of the polynomials used to…
In this paper, we propose new basis functions defined on curved sides or faces of curvilinear elements (polygons or polyhedrons with curved sides or faces) for the weak Galerkin finite element method. Those basis functions are constructed…
A conforming discontinuous Galerkin (DG) finite element method has been introduced in [21] on simplicial meshes, which has the flexibility of using discontinuous approximation and the simplicity in formulation of the classic continuous…
This paper presents an efficient weak Galerkin (WG) finite element method with reduced stabilizers for solving the time-harmonic Maxwell equations on both convex and non-convex polyhedral meshes. By employing bubble functions as a critical…
The weak Galerkin (WG) methods have been introduced in the references [11, 16] for solving the biharmonic equation. The purpose of this paper is to develop an algorithm to implement the WG methods effectively. This can be achieved by…
This paper presents a new weak Galerkin (WG) method for elliptic interface problems on general curved polygonal partitions. The method's key innovation lies in its ability to transform the complex interface jump condition into a more…
This paper is concerned with continuous and discrete approximations of $W^{2,p}$ strong solutions of second-order linear elliptic partial differential equations (PDEs) in non-divergence form. The continuous approximation of these equations…