Related papers: A stabilizer-free $C^0$ weak Galerkin method for t…
A new stabilizer free weak Galerkin (WG) method is introduced and analyzed for the biharmonic equation. Stabilizing/penalty terms are often necessary in the finite element formulations with discontinuous approximations to ensure the…
In this article, we decrease the degree of the polynomials on the boundary of the weak functions and modify the definition of the weak laplacian which are introduced in \cite{BiharmonicSFWG} to use the SFWG method for the biharmonic…
A C^0-weak Galerkin (WG) method is introduced and analyzed for solving the biharmonic equation in 2D and 3D. A weak Laplacian is defined for C^0 functions in the new weak formulation. This WG finite element formulation is symmetric,…
In this article, the stabilizer free weak Galerkin (SFWG) finite element method is applied to the Ciarlet-Raviart mixed form of the Biharmonic equation. We utilize the SFWG solutions of the second elliptic problems to define projection…
This paper presents a simplified weak Galerkin (WG) finite element method for solving biharmonic equations avoiding the use of traditional stabilizers. The proposed WG method supports both convex and non-convex polytopal elements in finite…
A new weak Galerkin (WG) finite element method is introduced and analyzed in this paper for the biharmonic equation in its primary form. This method is highly robust and flexible in the element construction by using discontinuous piecewise…
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…
The weak Galerkin (WG) finite element method is an effective and flexible general numerical technique for solving partial differential equations. It is a natural extension of the classic conforming finite element method for discontinuous…
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…
This paper presents a new and efficient numerical algorithm for the biharmonic equation by using weak Galerkin (WG) finite element methods. The WG finite element scheme is based on a variational form of the biharmonic equation that is…
A new weak Galerkin (WG) finite element method for solving the biharmonic equation in two or three dimensional spaces by using polynomials of reduced order is introduced and analyzed. The WG method is on the use of weak functions and their…
Recently, a new stabilizer free weak Galerkin method (SFWG) is proposed, which is easier to implement. The idea is to raise the degree of polynomials j for computing weak gradient. It is shown that if j>=j0 for some j0, then SFWG achieves…
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 paper presents an arbitrary order locking-free numerical scheme for linear elasticity on general polygonal/polyhedral partitions by using weak Galerkin (WG) finite element methods. Like other WG methods, the key idea for the linear…
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 introduces an auto-stabilized weak Galerkin (WG) finite element method for solving Stokes equations without relying on traditional stabilizers. The proposed WG method accommodates both convex and non-convex polytopal elements in…
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…
A weak Galerkin (WG) finite element method for solving the stationary Stokes equations in two- or three- dimensional spaces by using discontinuous piecewise polynomials is developed and analyzed. The variational form we considered is based…
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…