We derive error estimates in the L2 norms, for the streamline diffusion (SD) and discontinuous Galerkin (DG) finite element methods for steady state, energy dependent, Fermi equation in three space dimensions. These estimates yield optimal convergence rates due to the maximal available regularity of the exact solution. Here our focus is on theoretical aspects of the h and hp approximations in b...

A finite element based level set method is proposed for structural topology optimization. Because both the level set equation and the reinitialization equation are advection dominated partial differential equations, the standard Galerkin finite element method may produce oscillating results. In this paper, both equations are solved using a streamline diffusion finite element method (SDFEM). The...

A rarefied gas flow through a channel with arbitrary cross section is studied based on the BGK model. The discrete velocity and streamline diffusion finite element methods are combined to yield a numerical scheme. For this method we derive stability and optimal error estimates in the L2 norm. The optimality is due to the maximal available regularity of the exact solution for the corresponding h...

Laminar dispersion in a serpentine microchannel with a Y-shape inlet was investigated using optical coherence tomography (OCT) and optical Doppler tomography (ODT). Dimensionless analysis was performed to understand the complex convective diffusion phenomena. It was shown that OCT/ODT is not only a visualization method but also a methodology to characterize important physics: streamwise velocit...

In this article, we analyze the fractional-step θ method for the time-dependent convectiondiffusion equation. In our implementation, we completely separate the convection operator from the diffusion operator, and stabilize the convective solve using a streamline upwinded PetrovGalerkin (SUPG) method. We establish a priori error estimates and show that optimal values of θ yield a scheme that is ...

In this work, we propose a residual-based posteriori error estimator for algebraic flux-corrected (AFC) schemes stationary convection-diffusion equations. A global upper bound is derived the in energy norm general choice of limiter, which defines nonlinear stabilization term. diffusion-dominated regime, has same convergence properties as true error. second approach discussed, where way using St...

We introduce a fibre tractography framework based on a particle filter which estimates a local geometrical model of the underlying white matter tract, formulated as a 'streamline flow' using generalized helicoids. The method is not dependent on the diffusion model, and is applicable to diffusion tensor (DT) data as well as to high angular resolution reconstructions. The geometrical model allows...