The spline collocation method is used to approximate solutions of boundary value problems. The convergence analysis is given and the method is shown to have second-order convergence. A numerical illustration is given to show the pertinent features of the technique.  

in this paper, the boundary-based estimation of pressure distribution in the cardiovascular system is investigated using two dimensional flow images. the conventional methods of non-invasive estimation of pressure distribution in the cardiovascular flow domain use the differential form of governing equations. this study evaluates the advantages of using the integral form of the equations in the...

Lada et al. recently presented a detailed near-infrared extinction map of Globule G2 in the Coalsack molecular cloud complex, showing that this starless core has a well-defined central extinction minimum. We propose a model for G2 in which a rapid increase in external pressure is driving an approximately symmetric compression wave into the core. The rapid increase in external pressure could ari...

The recently introduced multiscale finite element method for solving elliptic equations with oscillating coefficients is designed to capture the large-scale structure of the solutions without resolving all the fine-scale structures. Motivated by the numerical simulation of flow transport in highly heterogeneous porous media, we propose a mixed multiscale finite element method with an over-sampl...

We investigate the existence, convergence and uniqueness of modified general curvature flow (MGCF) of convex hypersurfaces in hyperbolic space with a prescribed asymptotic boundary.

We report results from analog laboratory experiments, in which a large-scale flow is imposed upon natural convection from a hot boundary layer at the base of a large tank of corn syrup. The experiments show that the subdivision of the convective flow into four regions provides a reasonable conceptual framework for interpreting the effects of large-scale flow on plumes. Region I includes the are...

This report performs a complete analysis of convergence and rates of convergence of finite element approximations of the Navier-Stokes-α (NS-α) regularization of the NSE, under a zero-divergence constraint on the velocity, to the true solution of the NSE. Convergence of the discrete NS-α approximate velocity to the true Navier-Stokes velocity is proved and rates of convergence derived, under no...