相关论文: Generalized Multiscale Finite Element Method for E…

The finite element methods (FEM) are important techniques in engineering for solving partial differential equations, but they depend heavily on element shape quality for stability and good performance. In this paper, we introduce the…

In this paper, we develop the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) for convection-diffusion equations with inhomogeneous Dirichlet, Neumann and Robin boundary conditions, along with…

This paper is concerned with the design, analysis and implementation of preconditioning concepts for spectral Discontinuous Galerkin discretizations of elliptic boundary value problems. While presently known techniques realize a growth of…

We introduce an $hp$-version symmetric interior penalty discontinuous Galerkin finite element method (DGFEM) for the numerical approximation of the biharmonic equation on general computational meshes consisting of polygonal/polyhedral…

We present a new line-based discontinuous Galerkin (DG) discretization scheme for first- and second-order systems of partial differential equations. The scheme is based on fully unstructured meshes of quadrilateral or hexahedral elements,…

This paper provides the semi-discrete scheme by the central local discontinuous Galerkin method for space fractional diffusion equation on two sets of overlapping cells, and then we give the stability analysis and error estimates for the…

We combine continuous and discontinuous Galerkin methods in the setting of a model diffusion problem. Starting from a hybrid discontinuous formulation, we replace element interiors by more general subsets of the computational domain -…

We describe a new finite element method (FEM) to construct continuous equilibrium distribution functions of stellar systems. The method is a generalization of Schwarzschild's orbit superposition method from the space of discrete functions…

We develop a cut Discontinuous Galerkin method (cutDGM) for a diffusion-reaction equation in a bulk domain which is coupled to a corresponding equation on the boundary of the bulk domain. The bulk domain is embedded into a structured,…

In this paper, we propose a novel iterative multiscale framework for solving high-contrast contact problems of Signorini type. The method integrates the constrained energy minimizing generalized multiscale finite element method (CEM-GMsFEM)…

We propose, analyze mathematically, and study numerically a novel approach for the finite element approximation of the spectrum of second-order elliptic operators. The main idea is to reduce the stiffness of the problem by subtracting a…

In this paper, for the generalized Darcy problem (an elliptic equation with discontinuous coefficients), we study a special partial Least-Squares (Galerkin-least-squares) method, known as the augmented mixed finite element method, and its…

Spacetime Discontinuous Galerkin (DG) methods are used to solve hyperbolic PDEs describing wavelike physical phenomena. When the PDEs are nonlinear, the speed of propagation of the phenomena, called the wavespeed, at any point in the…

Discontinuous Galerkin (DG) methods offer an enormous flexibility regarding local grid refinement and variation of polynomial degrees for a variety of different problem classes. With a focus on diffusion problems, we consider DG…

In this paper, we construct a combined multiscale finite element method (MsFEM) using the Local Orthogonal Decomposition (LOD) technique to solve the multiscale problems which may have singularities in some special portions of the…

In this paper we present a new multiscale discontinuous Petrov--Galerkin method (MsDPGM) for multiscale elliptic problems. This method utilizes the classical oversampling multiscale basis in the framework of Petrov--Galerkin version of…

In this paper we propose a new finite element discretization for the two-field formulation of poroelasticity which uses the elastic displacement and the pore pressure as primary variables. The main goal is to develop a numerical method with…

In this paper, a time-domain discontinuous Galerkin (TDdG) finite element method for the full system of Maxwell's equations in optics and photonics is investigated, including a complete proof of a semi-discrete error estimate. The new…

In this paper, a generalized finite element method (GFEM) with optimal local approximation spaces for solving high-frequency heterogeneous Helmholtz problems is systematically studied. The local spaces are built from selected eigenvectors…

We develop a conservative cut finite element method for an elliptic coupled bulk-interface problem. The method is based on a discontinuous Galerkin framework where stabilization is added in such a way that we retain conservation on macro…