相关论文: Decoupled finite element methods for a fourth-orde…
Arnold, Falk, & Winther, in "Finite element exterior calculus, homological techniques, and applications" (2006), show how to geometrically decompose the full and trimmed polynomial spaces on simplicial elements into direct sums of…
We hybridize the methods of finite element exterior calculus for the Hodge-Laplace problem on differential $k$-forms in $\mathbb{R}^n$. In the cases $k = 0$ and $k = n$, we recover well-known primal and mixed hybrid methods for the scalar…
This paper will suggest a new finite element method to find a $P^4$-velocity and a $P^3$-pressure solving Stokes equations. The method solves first the decoupled equation for the $P^4$-velocity. Then, four kinds of local $P^3$-pressures and…
We present a new method for the analysis of electromagnetic scattering from homogeneous penetrable bodies. Our approach is based on a reformulation of the governing Maxwell equations in terms of two uncoupled vector Helmholtz systems: one…
Finite element exterior calculus refers to the development of finite element methods for differential forms, generalizing several earlier finite element spaces of scalar fields and vector fields to arbitrary dimension $n$, arbitrary…
The modified biharmonic equation is encountered in a variety of application areas, including streamfunction formulations of the Navier-Stokes equations. We develop a separation of variables representation for this equation in polar…
Fourth-order differential equations play an important role in many applications in science and engineering. In this paper, we present a three-field mixed finite-element formulation for fourth-order problems, with a focus on the effective…
A method is presented that reduces the number of terms of systems of linear equations (algebraic, ordinary and partial differential equations). As a byproduct these systems have a tendency to become partially decoupled and are more likely…
The so-called method of phase synchronization has been advocated in a number of papers as a way of decoupling a system of linear second-order differential equations by a linear transformation of coordinates and velocities. This is a rather…
In this paper, we consider the extension of the finite element exterior calculus from elliptic problems, in which the Hodge Laplacian is an appropriate model problem, to parabolic problems, for which we take the Hodge heat equation as our…
In the framework of a mixed finite element method, a structure-preserving formulation for incompressible magnetohydrodynamic (MHD) equations with general boundary conditions is proposed. A leapfrog-type temporal scheme fully decouples the…
A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…
This work is about a new two-level solver for Helmholtz equations discretized by finite elements. The method is inspired by two-grid methods for finite-difference Helmholtz problems as well as by previous work on two-level…
In this paper, we consider the numerical approximation for a diffuse interface model of the two-phase incompressible inductionless magnetohydrodynamics problem. This model consists of Cahn-Hilliard equations, Navier-Stokes equations and…
Our work is about energy conserving fourth-order time discretizations of a three-field formulation of Maxwell's equations in conjunction with a spatial discretization using higher-order and compatible de Rham finite element spaces. Toward…
Mixed finite element methods are considered for a ferrofluid flow model with magnetization paralleled to the magnetic field. The ferrofluid model is a coupled system of the Maxwell equations and the incompressible Navier-Stokes equations.…
This article surveys research on the application of compatible finite element methods to large scale atmosphere and ocean simulation. Compatible finite element methods extend Arakawa's C-grid finite difference scheme to the finite element…
A finite element approach for approximating the solution of a mathematical model for the response of a penetrable, bounded object (obstacle) to the excitation by an external electromagnetic field is presented and investigated. The model…
In this article, we have developed a higher order compact numerical method for variable coefficient parabolic problems with mixed derivatives. The finite difference scheme, presented here for two-dimensional domains, is based on fourth…
An efficient numerical method is proposed for computing the Dirichlet-to-Neumann (DtN) map associated with the exterior Dirichlet problem for the two-dimensional Helmholtz equation with an inhomogeneous term. The exterior solution is…