Related papers: A Weak Galerkin Method for Elasticity Interface Pr…
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…
This article develops a weak Galerkin least-squares (WG--LS) finite element method for first-order linear convection equations in non-divergence form. The method is formulated using discontinuous finite element functions and does not…
This paper introduces and rigorously analyzes a least-squares weak Galerkin (LS-WG) finite element method for the severely ill-posed Cauchy problem associated with the Helmholtz equation. By utilizing a weak Laplacian operator defined on a…
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…
This paper is concerned with the development of weak Galerkin (WG) finite element method for optimal control problems governed by second order elliptic partial differential equations (PDEs). It is advantageous to use discontinuous finite…
In this paper, authors shall introduce a finite element method by using a weakly defined gradient operator over discontinuous functions with heterogeneous properties. The use of weak gradients and their approximations results in a new…
This article is devoted to computing the eigenvalue of the Laplace eigenvalue problem by the weak Galerkin (WG) finite element method with emphasis on obtaining lower bounds. The WG method is on the use of weak functions and their weak…
This paper introduces an auto-stabilized weak Galerkin (WG) finite element method for biharmonic equations with built-in stabilizers. Unlike existing stabilizer-free WG methods limited to convex elements in finite element partitions, our…
The generalized weak Galerkin (gWG) finite element method is proposed and analyzed for the biharmonic equation. A new generalized discrete weak second order partial derivative is introduced in the gWG scheme to allow arbitrary combinations…
The weak Galerkin (WG) finite element method is an effective and flexible general numerical techniques for solving partial differential equations. A simple weak Galerkin finite element method is introduced for second order elliptic…
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, the weak Galerkin finite element method for second order elliptic problems employing polygonal or polyhedral meshes with arbitrary small edges or faces was analyzed. With the shape regular assumptions, optimal convergence…
The weak Galerkin finite element method is a novel numerical method that was first proposed and analyzed by Wang and Ye for general second order elliptic problems on triangular meshes. The goal of this paper is to conduct a computational…
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…
In this paper a hybridized weak Galerkin (HWG) finite element method for solving the Stokes equations in the primary velocity-pressure formulation is introduced. The WG method uses weak functions and their weak derivatives which are defined…
In this paper, a new and efficient numerical algorithm by using weak Galerkin (WG) finite element methods is proposed for a type of fourth order problem arising from fluorescence tomography(FT). Fluorescence tomography is an emerging, in…
This paper introduces an auto-stabilized weak Galerkin (WG) finite element method with a built-in stabilizer for Poisson equations. By utilizing bubble functions as a key analytical tool, our method extends to both convex and non-convex…
We present a weak finite element method for elliptic problems in one space dimension. Our analysis shows that this method has more advantages than the known weak Galerkin method proposed for multi-dimensional problems, for example, it has…
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…
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…