We provide the first a priori error analysis of a hybridizable discontinuous Galerkin (HDG) method for solving the vorticity-velocity-pressure formulation of the three-dimensional Stokes equations of incompressible fluid flow. By using a projection-based approach, we prove that, when all the unknowns use polynomials of degree k ≥ 0, the L2 − norm of the errors in the approximate vorticity and p...

where the unknown f(t, x, v) is a nonnegative integrable function standing for the density of particles in phase space : time t ≥ 0, position x ∈ R, velocity v ∈ R, n ≥ 2. More precisely, this first part is devoted to some properties linked with the operator from (1.13) below, which is linked with one possible weak formulation of Boltzmann equation (1.1). On the right hand side of (1.1), Q is t...

A dual formulation and finite element method is proposed and analyzed for simulating the Stefan problem with surface tension. The method uses a mixed form of the heat equation in the solid and liquid (bulk) domains, and imposes a weak formulation of the interface motion law (on the solidliquid interface) as a constraint. The basic unknowns are the heat fluxes and temperatures in the bulk, and t...

The paper considers receiving acoustic horns designed for particle velocity amplification and suitable for use in vector sensing applications. Unlike conventional horns, designed for acoustic pressure amplification, acoustic velocity horns (AVHs) deliver significant velocity amplification even when the overall size of the horn is much less than an acoustic wavelength. An AVH requires an open-en...

We develop a level set method for the computation of multi-valued velocity and electric fields of one-dimensional Euler-Poisson equations. The system of these equations arises in the semiclassical approximation of SchrödingerPoisson equations and semiconductor modeling. This method uses an implicit Eulerian formulation in an extended space — called field space, which incorporates both velocity ...

An algorithm is proposed for the computation of streamfunction and velocity potential from given horizontal velocity vectors based on solving a minimization problem. To guarantee the uniqueness of the solution and computational reliability of the algorithm, a Tikhonov regularization is applied. The solution implies that the obtained streamfunction and velocity potential have minimal magnitude, ...

It is proved that the cosmological density perturbation is associated with a peculiar velocity field. This allows a simple formulation of cosmological perturbation theory, which works entirely with quasi-Newtonian fluid flow equations. As an illustration, the large scale cosmic microwave background anisotropy (Sachs-Wolfe effect) is calculated without any reference to the metric perturbation. I...

Bottom boundary layer effects on the linear wave propagation over mild slope bottoms are analyzed. A modifiedWKB approximation is presented including boundary layer effects. Within the boundary layer, two cases are considered: laminar (constant viscosity) and turbulent. Boundary layer effects are introduced by coupling the velocity inside the boundary layer to the irrotational velocity in the c...

We have studied the statistical mechanics of money circulation in a closed economic system. An explicit statistical formulation of the circulation velocity of money is presented for the first time by introducing the concept of holding time of money. The result indicates that the velocity is governed by behavior patterns of economic agents. Computer simulations have been carried out in order to ...

This paper investigates the applicability of prestack Stolt residual migration when the original image is obtained using an arbitrary velocity model. At its origin, the method is based on an assumption of constant velocity. However, its formulation for depth-migrated images involves a ratio of the reference and target velocities; therefore, for residual migration it is completely irrelevant if ...