Given a convex polygon P in the projective plane we can form a finite “grid” of points by taking the pairwise intersections of the lines extending the edges of P . When P is a Poncelet polygon we show that this grid is contained in a finite union of ellipses and hyperbolas and derive other related geometric information about the grid.

I prove that a centre manifold approach to creating finite difference models will consistently model linear dynamics as the grid spacing becomes small. Using such tools of dynamical systems theory gives new assurances about the quality of finite difference models under nonlinear and other perturbations on grids with finite spacing. For example, the linear advection-diffusion equation is found t...

In this paper, a moving mesh technique and a non-standard finite difference method are combined, and a moving mesh non-standard finite difference (MMNSFD) method is developed to solve an initial boundary value problem involving a quartic nonlinearity that arises in heat transfer with thermal radiation. In this method, the moving spatial grid is obtained by a simple geometric adaptive algorithm ...

n this work, computational fluid dynamics of the flow behavior in a cold flow of fluidized bed is studied. An improved finite volume based finite element method has been introduced to solve the two-phase gas/solid flow hydrodynamic equations. This method uses a collocated grid, where all variables are located at the nodal points. The fluid dynamic model for gas/solid two-phase flow is based on ...

We develop a finite element method for convection diffusion problems on a given time dependent surface, for instance modeling the evolution of a surfactant. The method is based on a characteristic-Galerkin formulation combined with a piecewise linear cut finite element method in space. The cut finite element method is constructed by embedding the surface in a background grid and then using the ...