Related papers: An Immersed Weak Galerkin Method for Elliptic Inte…
A parallelizable iterative procedure based on domain decomposition is presented and analyzed for weak Galerkin finite element methods for second order elliptic equations. The convergence analysis is established for the decomposition of the…
A Galerkin finite element method for the membrane elasticity problem on a meshed surface is constructed by using two-dimensional elements extended into three dimensions. The membrane finite element model is established using the intrinsic…
$H^1$-conforming Galerkin methods on polygonal meshes such as VEM, BEM-FEM and Trefftz-FEM employ local finite element functions that are implicitly defined as solutions of Poisson problems having polynomial source and boundary data.…
We consider the singularly perturbed fourth-order boundary value problem $\varepsilon ^{2}\Delta ^{2}u-\Delta u=f $ on the unit square $\Omega \subset \mathbb{R}^2$, with boundary conditions $u = \partial u / \partial n = 0$ on $\partial…
An interface/boundary-unfitted eXtended hybridizable discontinuous Galerkin (X-HDG) method of arbitrary order is proposed for linear elasticity interface problems on unfitted meshes with respect to the interface and domain boundary. 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…
This article presents new immersed finite element (IFE) methods for solving the popular second order elliptic interface problems on structured Cartesian meshes even if the involved interfaces have nontrivial geometries. These IFE methods…
This paper develops and analyzes a class of semi-discrete and fully discrete weak Galerkin finite element methods for unsteady incompressible convective Brinkman-Forchheimer equations. For the spatial discretization, the methods adopt the…
Spacetime discontinuous Galerkin (SDG) finite element methods are used to solve such PDEs involving space and time variables arising from wave propagation phenomena in important applications in science and engineering. To support an…
New finite element methods are proposed for elliptic interface problems in one and two dimensions. The main motivation is not only to get an accurate solution but also an accurate first order derivative at the interface (from each side).…
This paper introduces an efficient stabilizer-free weak Galerkin (WG) finite element method for solving the three-dimensional quad-curl problem. Leveraging bubble functions as a key analytical tool, the method extends the applicability of…
This paper presents a simple weak Galerkin (WG) finite element method for the Reissner-Mindlin plate model that partially eliminates the need for traditionally employed stabilizers. The proposed approach accommodates general, including…
Standard low-order finite elements, which perform well for problems involving compressible elastic materials, are known to under-perform when nearly incompressible materials are involved, commonly exhibiting the locking phenomenon. Interior…
In this paper, we propose two arbitrary order eXtended hybridizable Discontinuous Galerkin (X-HDG) methods for second order elliptic interface problems in two and three dimensions. The first X-HDG method applies to any piecewise $C^2$…
We present a compatible space-time hybridizable/embedded discontinuous Galerkin discretization for nonlinear free-surface waves. We pose this problem in a two-fluid (liquid and gas) domain and use a time-dependent level-set function to…
Weak Galerkin (WG) refers to general finite element methods for partial differential equations in which differential operators are approximated by weak forms through the usual integration by parts. In particular, WG methods allow the use of…
In this paper, we propose a novel mesh-free numerical method for solving the elliptic interface problems based on deep learning. We approximate the solution by the neural networks and, since the solution may change dramatically across the…
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)…
We propose an unfitted interface penalty Discontinuous Galerkin-Finite Element Method (UIPDG-FEM) for elliptic interface problems. This hybrid method combines the interior penalty discontinuous Galerkin (IPDG) terms near the…
This is the second paper on the study of gradient recovery for elliptic interface problem. In our previous work [H. Guo and X. Yang, 2016, arXiv:1607.05898], we developed gradient recovery finite element method based on body-fitted mesh. In…