We present a fourth-order compact finite difference scheme on the face centered cubic (FCC) grids for the numerical solution of the two-dimensional convection diffusion equation. The seven-point formula is defined on a regular hexagon, where the strategy of directional derivative is employed to make the derivation procedure straightforward, efficient, and concise. A corresponding multigrid meth...

We consider energy-conserving semi-discretizations of linear wave equations on nonuniform grids. Specifically we study explicit and implicit skew-adjoint finite difference methods, based on the assumption of an underlying smooth mapping from a uniform grid, applied to the first and second order wave equations. Our interest is in internal reflection of energy at abrupt variations in grid spacing...

A numerical model for electro-osmotic flow is described. The advecting velocity field is computed by solving the incompressible Navier–Stokes equation. The method uses a semi-implicit multigrid algorithm to compute the divergence-free velocity at each grid point. The finite differences are second-order accurate and centered in space; however, the traditional second-order compact finite differen...

We develop a finite element discretization for the weakly symmetric equations of linear elasticity on tetrahedral meshes. The finite element combines, for r ≥ 0, discontinuous polynomials of r for the displacement, H(div)-conforming polynomials of order r+1 for the stress, and H(curl)-conforming polynomials of order r + 1 for the vector representation of the multiplier. We prove that this tripl...

to control the nonlinear numerical instability, throughout the time evolution of the eulerian form of the nonlinear rotating shallow water equations, it is necessary to add numerical diffusion to the solution. it is clear that, this extra numerical diffusion degrades the accuracy of the numerical solution and should be kept as small as possible. in a conventional approach a hyper-diffusion is u...

We consider the product of a finite number of non-Hermitian random matrices with i.i.d. centered entries of growing size. We assume that the entries have a finite moment of order bigger than two. We show that the empirical spectral distribution of the properly normalized product converges, almost surely, to a non-random, rotationally invariant distribution with compact support in the complex pl...

In this paper we obtain a quantitative Voronovskaja result and the exact orders in approximation by the derivatives of complex Riesz-Zygmund means in compact disks. 2000 Mathematical Subject Classification: Primary : 30E10 ; Secondary : 41A25, 41A28.

the polarimetric entropy and the alpha angle are two important parameters for analyzing polarimetric synthetic aperture radar data. they demonstrate the degree of randomness in the polarization of the received signal and scattering mechanism of scatterers respectively. recently, there has been an increasing interest in compact polarimetry due to its advantages in comparison with full polarimetr...

We present 1300μmmaps of regions centered on the energy sources of 20 HH objects in order to study the distribution of circumstellar matter around these young stellar objects. The data show that the emission generally originates from a rather compact region which is embedded in a more diffuse environment. The relative contribution of the compact component to the total emission varies from 15 to...