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Finite difference
About: Finite difference is a research topic. Over the lifetime, 19693 publications have been published within this topic receiving 408603 citations.
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TL;DR: In this paper, the notion of finite singularities of difference operators is introduced, in order to adapt methods for differential equations to the case of recurrence equations, in which the singularity of the difference operator is replaced by a singularity.
104 citations
TL;DR: In this paper, it was shown that the GKS stability criterion has a physical interpretation in terms of group velocity, and that if the finite difference model together with its boundary conditions can support a set of waves at the boundary with group velocities pointing into the field then it is unstable.
104 citations
TL;DR: This paper considers iterative algorithms of Uzawa type for solving linear nonsymmetric saddle point problems, and considers systems, written as usual in block form, where the upper left block is an invertible linear operator with positive definite symmetric part.
Abstract: In this paper, we consider iterative algorithms of Uzawa type for solving linear nonsymmetric saddle point problems. Specifically, we consider systems, written as usual in block form, where the upper left block is an invertible linear operator with positive definite symmetric part. Such saddle point problems arise, for example, in certain finite element and finite difference discretizations of Navier-Stokes equations, Oseen equations, and mixed finite element discretization of second order convection-diffusion problems. We consider two algorithms, each of which utilizes a preconditioner for the operator in the upper left block. Convergence results for the algorithms are established in appropriate norms. The convergence of one of the algorithms is shown assuming only that the preconditioner is spectrally equivalent to the inverse of the symmetric part of the operator. The other algorithm is shown to converge provided that the preconditioner is a sufficiently accurate approximation of the inverse of the upper left block. Applications to the solution of steady-state Navier-Stokes equations are discussed, and, finally, the results of numerical experiments involving the algorithms are presented.
104 citations
TL;DR: The method developed in this article has been applied to obtain the numerical solutions of the lid driven cavity flow problem governed by the 2D incompressible Navier-Stokes equations using the stream function-vorticity formulation.
104 citations
TL;DR: In this article, an upstream finite element scheme is presented for overcoming the problem of numerical oscillations associated with the transient transport equation for convective dominated or purely convective flow, where spatial discretization is performed via a general weighted residual technique which employs asymmetric weighting functions and yields upstream weighting of the convective term in the transport equation.
104 citations