In this paper, we apply streamline-diffusion and Galerkin-least-squares finite element methods for 2D steady-state two-phase model in the cathode of polymer electrolyte fuel cell (PEFC) that contains a gas channel and a gas diffusion layer (GDL). This two-phase PEFC model is typically modeled by a modified Navier-Stokes equation for the mass and momentum, with Darcy’s drag as an additional sour...

Adaptive finite element methods for stationary convectiondiffusion problems are designed and analyzed. The underlying discretization scheme is the Shock-capturing Streamline Diffusion method. The adaptive algorithms proposed are based on a posteriori error estimates for this method leading to reliable methods in the sense that the desired error control is guaranteed. A priori error estimates ar...

The purpose of the paper is to introduce a novel cell boundary element (CBE) method for the convection dominated diffusion equation. The CBE method can be viewed as a Petrov-Galerkin type method defined on the skeleton of a mesh. The proposed method utilizes continuity of normal flux on each inter-element boundary. By constructing a local basis (mesh-oriented element) that is dependent upon the...

We derive error estimates in the appropriate norms, for the streamlinediffusion (SD) finite element methods for steady state, energy dependent,Fermi equation in three space dimensions. These estimates yield optimal convergencerates due to the maximal available regularity of the exact solution.High order SD method together with implicit integration are used. The formulationis strongly consistent...

The choice of geometrical shape of the blades has a considerable effect on aerodynamic performance and flow characteristics in axial compressors. In this paper, the effects of the blades shape on the aerodynamic design characteristics are investigated based on Streamline Curvature Method (SCM). Initially, the Streamline Curvature Method (SCM) is used for designing a two-stage axial compressor. ...

In this paper local discontinuous Galerkin method (LDG) was analyzed for solving 1-D convection-diffusion equations with a boundary layer near the outflow boundary. Local error estimates are established on quasi-uniform meshes with maximum mesh size h. On a subdomain with O(h ln(1/h)) distance away from the outflow boundary, the L error of the approximations to the solution and its derivative c...

A methodology is presented for estimation of a probability density function of cerebral fibre orientations when one or two fibres are present in a voxel. All data are acquired on a clinical MR scanner, using widely available acquisition techniques. The method models measurements of water diffusion in a single fibre by a Gaussian density function and in multiple fibres by a mixture of Gaussian d...

We compute the front speeds of the Kolmogorov-Petrovsky-Piskunov (KPP) reactive fronts in two prototypes of periodic incompressible flows (the cellular flows and the cat’s eye flows). The computation is based on adaptive streamline diffusion methods for the advection-diffusion type principal eigenvalue problem associated with the KPP front speeds. In the large amplitude regime, internal layers ...

We present a stabilized finite element method for the scalar advection-diffusion equation, which does not require tunable mesh-dependent parameters. Stabilization is achieved by using diffusive fluxes extracted from an edge element lifting of Scharfetter-Gummel edge fluxes into the elements. Although the method is formally first-order accurate, qualitative numerical studies suggest that it occu...

Introduction: Spatial normalisation of diffusion data allows diffusion properties to be compared across a population without any bias from macrostructural differences in tissue anatomy. Standard approaches perform spatial normalisation of diffusion tensors. However streamline tractography through lattices of tensors is mainly suited to reconstruction of major white matter fibres. In contrast pr...