Related papers: A Least Squares Method for Linear Elasticity using…
We propose a new least squares finite element method to solve the Stokes problem with two sequential steps. The approximation spaces are constructed by patch reconstruction with one unknown per element. For the first step, we reconstruct an…
In this paper, we propose and analyze the least squares finite element methods for the linear elasticity interface problem in the stress-displacement system on unfitted meshes. We consider the cases that the interface is $C^2$ or polygonal,…
We propose a new discontinuous Galerkin method based on the least-squares patch reconstruction for the biharmonic problem. We prove the optimal error estimate of the proposed method. The two-dimensional and three-dimensional numerical…
In this article, using the weighted discrete least-squares, we propose a patch reconstruction finite element space with only one degree of freedom per element. As the approximation space, it is applied to the discontinuous Galerkin methods…
We propose a discontinuous Galerkin(DG) method to approximate the elliptic interface problem on unfitted mesh using a new approximation space. The approximation space is constructed by patch reconstruction with one degree of freedom per…
We propose a new least squares finite element method to solve the Poisson equation. By using a piecewisely irrotational space to approximate the flux, we split the classical method into two sequential steps. The first step gives the…
In this paper, we study a mixed discontinuous Galerkin (MDG) method to solve linear elasticity problem with arbitrary order discontinuous finite element spaces in $d$-dimension ($d=2,3$). This method uses polynomials of degree $k+1$ for the…
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…
We adapt a symmetric interior penalty discontinuous Galerkin method using a patch reconstructed approximation space to solve elliptic eigenvalue problems, including both second and fourth order problems in 2D and 3D. It is a direct…
We propose a discontinuous least squares finite element method for solving the Helmholtz equation. The method is based on the L2 norm least squares functional with the weak imposition of the continuity across the interior faces as well as…
A discontinuous Galerkin method by patch reconstruction is proposed for Stokes flows. A locally divergence-free reconstruction space is employed as the approximation space, and the interior penalty method is adopted which imposes the normal…
We present an arbitrary order discontinuous Galerkin finite element method for solving the biharmonic interface problem on the unfitted mesh. The approximation space is constructed by a patch reconstruction process with at most one degree…
We propose a least-squares method involving the recovery of the gradient and possibly the Hessian for elliptic equation in nondivergence form. As our approach is based on the Lax--Milgram theorem with the curl-free constraint built into the…
We propose an arbitrary-order discontinuous Galerkin method for second-order elliptic problem on general polygonal mesh with only one degree of freedom per element. This is achieved by locally solving a discrete least-squares over a…
We propose and analyze a discontinuous least squares finite element method for solving the indefinite time-harmonic Maxwell equations. The scheme is based on the $L^2$ norm least squares functional with the weak imposition of the continuity…
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…
An hyperelastic biphasic model is presented. For slow-draining problems (permeability less than 1\times10-2 mm4 N-1 s-1), numerical instabilities in the form of non-physical oscillations in the pressure field are observed in 3D problems…
A convergence result for a discontinuous Galerkin multiscale method for a second order elliptic problem is presented. We consider a heterogeneous and highly varying diffusion coefficient in $L^\infty(\Omega,\mathbb{R}^{d\times d}_{sym})$…
In this paper, we develop an efficient preconditioned unfitted finite element method for the elliptic interface problem, based on the reconstructed discontinuous approximation. The approximation method for interface problems is originally…
In this work, we propose and investigate stable high-order collocation-type discretisations of the discontinuous Galerkin method on equidistant and scattered collocation points. We do so by incorporating the concept of discrete least…