A mathematical and numerical model describing chemical transport in a Stokes– Darcy flow system is discussed. The flow equations are solved through domain decomposition using classical finite element methods in the Stokes region and mixed finite element methods in the Darcy region. The local discontinuous Galerkin (LDG) method is used to solve the transport equation. Models dealing with couplin...

in this paper, optimal distributed control of the time-dependent navier-stokes equations is considered. the control problem involves the minimization of a measure of the distance between the velocity field and a given target velocity field. a mixed numerical method involving a quasi-newton algorithm, a novel calculation of the gradients and an inhomogeneous navier-stokes solver, to find the opt...

In O(3) symmetry electrodynamics the field tensor is governed by a nonAbelian Stokes Theorem, as in any non-Abelian gauge theory. The comments on the B component of this field tensor by Hunter in this Issue address B as if it were a U(1) symmetry field, governed by the ordinary Stokes Theorem, and are therefore sequentially erroneous, because there is a basic misunderstanding of the nature of O...

It is shown that the generalization of the Navier-Stokes equations to a theory with N “internal state” copies of the velocity fields is a step in a wrong direction: the N → ∞ limit has no physical sense and produces wrong results, whereas the treatment of the first order terms in 1/N is even more complicated than the initial problem of description of turbulence in the frame of the Navier-Stokes...

In this paper we describe two recent approaches for the Lp-theory of the Navier-Stokes flow in the exterior of a moving or rotating obstacle.

A mixed finite element method for the Navier–Stokes equations is introduced in which the stress is a primary variable. The variational formulation retains the mathematical structure of the Navier–Stokes equations and the classical theory extends naturally to this setting. Finite element spaces satisfying the associated inf–sup conditions are developed. Mathematics Subject Classification. 65N60,...

This article studies two methods for obtaining excellent mass conservation in finite element computations of the Navier-Stokes equations using continuous velocity fields. With a particular mesh construction, the Scott-Vogelius element pair has recently been shown to be inf-sup stable and have optimal approximation properties, while also providing pointwise mass conservation. We present herein t...

For Stokes problem, we show how to obtain nite volume schemes from a Mixed nite element method with a well chosen numerical integration diagonalising the mass matrix. The analysis of the corresponding nite volume scheme is directly deduced from general results of mixed nite element theory. In this note, we exhibit nite volume scheme for Stokes problem and give optimal a priori error estimate. R...

We explore theoretically and numerically optical rogue wave formation in stimulated Raman scattering inside a hydrogen filled hollow core photonic crystal fiber. We assume a weak noisy Stokes pulse input and explicitly construct the input Stokes pulse ensemble using the coherent mode representation of optical coherence theory, thereby providing a link between optical coherence and rogue wave th...

We discuss the application of complex variable methods to Hele-Shaw flows and twodimensional Stokes flows, both with free boundaries. We outline the theory for the former, in the case where surface tension effects at the moving boundary are ignored. We review the application of complex variable methods to Stokes flows both with and without surface tension, and we explore the parallels between t...