相关论文: Lowest-order equivalent nonstandard finite element…
A unified framework for fourth-order semilinear problems with trilinear nonlinearity and general source allows for quasi-best approximation with lowest-order finite element methods. This paper establishes the stability and a priori error…
The lowest-order nonconforming virtual element extends the Morley triangular element to polygons for the approximation of the weak solution $u\in V:=H^2_0(\Omega)$ to the biharmonic equation. The abstract framework allows (even a mixture…
The Morley finite element method (FEM) is attractive for semilinear problems with the biharmonic operator as a leading term in the stream function vorticity formulation of 2D Navier-Stokes problem and in the von K\'{a}rm\'{a}n equations.…
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…
This paper studies the nonconforming Morley finite element approximation of the eigenvalues of the biharmonic operator. A new $C^1$ conforming companion operator leads to an $L^2$ error estimate for the Morley finite element method which…
This paper presents a nonconforming finite element scheme for the planar biharmonic equation which applis piecewise cubic polynomials ($P_3$) and possesses $\mathcal{O}(h^2)$ convergence rate in energy norm on general shape-regular…
In this paper, we present a high-order finite element method based on a reconstructed approximation to the biharmonic equation. In our construction, the space is reconstructed from nodal values by solving a local least squares fitting…
This paper deals with the numerical approximation of the biharmonic inverse source problem in an abstract setting in which the measurement data is finite-dimensional. This unified framework in particular covers the conforming and…
We consider the Weak Galerkin finite element approximation of the Singularly Perturbed Biharmonic elliptic problem on a unit square domain with clamped boundary conditions. Shishkin mesh is used for domain discretization as the solution…
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 paper we address the numerical approximation of linear fourth-order elliptic problems on polygonal meshes. In particular, we present a novel nonconforming virtual element discretization of arbitrary order of accuracy for biharmonic…
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…
We develop a basic convergence analysis for an adaptive $\textsf{C}^0\textsf{IPG}$ method for the Biharmonic problem, which provides convergence without rates for all practically relevant marking strategies and all penalty parameters…
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,…
A general a posteriori error analysis applies to five lowest-order finite element methods for two fourth-order semi-linear problems with trilinear non-linearity and a general source. A quasi-optimal smoother extends the source term to the…
In this paper, we present a study on the effect of penalty term in the mixed Discontinuous Galerkin Finite Element Method for the biharmonic equation proposed by \cite{gudi2008mixed}. The proposed mixed Discontinuous Galerkin Method showed…
The symmetric $C^0$ interior penalty method is one of the most popular discontinuous Galerkin methods for the biharmonic equation. This paper introduces an automatic local selection of the involved stability parameter in terms of the…
This paper introduces a new weak Galerkin (WG) finite element method for second order elliptic equations on polytopal meshes. This method, called WG-FEM, is designed by using a discrete weak gradient operator applied to discontinuous…
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 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…