Related papers: A Weak Galerkin Mixed Finite Element Method for Bi…
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…
A stabilizing/penalty term is often used in finite element methods with discontinuous approximations to enforce connection of discontinuous functions across element boundaries. Removing stabilizers from discontinuous finite element methods…
A new $H(\textrm{divdiv})$-conforming finite element is presented, which avoids the need for super-smoothness by redistributing the degrees of freedom to edges and faces. This leads to a hybridizable mixed method with superconvergence for…
This article introduces a simple weak Galerkin (WG) finite element method for solving convection-diffusion-reaction equation. The proposed method offers significant flexibility by supporting discontinuous approximating functions on general…
The mixed finite element method for the Poisson problem with the Raviart-Thomas elements of low-level can be interpreted as a finite volume method with a non-local gradient. In this contribution, we propose a variant of Petrov-Galerkin type…
A new primal-dual weak Galerkin (PD-WG) finite element method was developed and analyzed in this article for first-order linear convection equations in non-divergence form. The PD-WG method results in a symmetric discrete system involving…
This paper considers weak Galerkin finite element approximations for a quasistatic Maxwell viscoelastic model. The spatial discretization uses piecewise polynomials of degree $k \ (k\geq 1)$ for the stress approximation, degree $k+1$ for…
In this paper, the authors devise a new discretization scheme for div-curl systems defined in connected domains with heterogeneous media by using the weak Galerkin finite element method. Two types of boundary value problems are considered…
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,…
This article presents a new primal-dual weak Galerkin finite element method for the div-curl system with tangential boundary conditions and low-regularity assumptions on the solution. The numerical scheme is based on a weak variational form…
An adaptive modified weak Galerkin method (AmWG) for an elliptic problem is studied in this paper, in addition to its convergence and optimality. The modified weak Galerkin bilinear form is simplified without the need of the skeletal…
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…
We extend the finite element method introduced by Lakkis and Pryer [2011] to approximate the solution of second order elliptic problems in nonvariational form to incorporate the discontinuous Galerkin (DG) framework. This is done by viewing…
This paper is concerned with finite element approximations of $W^{2,p}$ strong solutions of second-order linear elliptic partial differential equations (PDEs) in non-divergence form with continuous coefficients. A nonstandard (primal)…
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…
The popular (piecewise) quadratic schemes for the biharmonic equation based on triangles are the nonconforming Morley finite element, the discontinuous Galerkin, the $C^0$ interior penalty, and the WOPSIP schemes. Those methods are modified…
A modified primal-dual weak Galerkin (M-PDWG) finite element method is designed for the second order elliptic equation in non-divergence form. Compared with the existing PDWG methods proposed in \cite{wwnondiv}, the system of equations…
In this paper, we present an immersed weak Galerkin method for solving second-order elliptic interface problems. The proposed method does not require the meshes to be aligned with the interface. Consequently, uniform Cartesian meshes can be…
We propose a boundary-corrected weak Galerkin mixed finite element method for solving elliptic interface problems in 2D domains with curved interfaces. The method is formulated on body-fitted polygonal meshes, where interface edges are…
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…