Topic
Finite difference method
About: Finite difference method is a research topic. Over the lifetime, 21603 publications have been published within this topic receiving 468852 citations. The topic is also known as: Finite-difference methods & FDM.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this article, a finite difference operator approximating second derivatives and satisfying a summation by parts rule was derived for the fourth, sixth and eighth order case by using the symbolic mathematics software Maple.
394 citations
TL;DR: In this article, a new boundary condition was proposed for beam propagation calculations that passes outgoing radiation freely with minimum reflection coefficient (as low as 3*10/sup -8/).
Abstract: A new boundary condition is presented for use in beam propagation calculations that passes outgoing radiation freely with minimum reflection coefficient (as low as 3*10/sup -8/). In conjunction with a standard Crank-Nicholson finite difference scheme, the assumption that the radiation field behaves as a complex exponential near the boundary is shown to result in a specific transparent boundary condition algorithm. In contrast to the commonly used absorber method, this algorithm contains no adjustable parameters, and is thus problem independent. It is shown to be accurate and robust for both two- and three-dimensional problems. >
392 citations
TL;DR: Two a posteriori error estimators for the mini-element discretization of the Stokes equations are presented, based on a suitable evaluation of the residual of the finite element solution, which are globally upper and locally lower bounds for the error of the infinite element discretized.
Abstract: We present two a posteriori error estimators for the mini-element discretization of the Stokes equations. One is based on a suitable evaluation of the residual of the finite element solution. The other one is based on the solution of suitable local Stokes problems involving the residual of the finite element solution. Both estimators are globally upper and locally lower bounds for the error of the finite element discretization. Numerical examples show their efficiency both in estimating the error and in controlling an automatic, self-adaptive mesh-refinement process. The methods presented here can easily be generalized to the Navier-Stokes equations and to other discretization schemes.
387 citations
TL;DR: In this article, a numerical method to simulate liquid-vapor phase change is presented, based on the so-called single field formulation where one set of equations for conservation of mass, momentum and energy are written for the entire flow field.
383 citations