The aim of this paper is to study the convergence analysis of three low order Crouzeix-Raviart type nonconforming rectangular finite elements to Maxwell’s equations, on a mixed finite element scheme and a finite element scheme, respectively. The error estimates are obtained for one of above elements with regular meshes and the other two under anisotropic meshes, which are as same as those in th...

We study the ability of high order numerical methods to propagate discrete waves at the same speed as the physical waves in the case of the one-way wave equation. A detailed analysis of the finite element method is presented including an explicit form for the discrete dispersion relation and a complete characterisation of the numerical Bloch waves admitted by the scheme. A comparision is made w...

This paper describes a characteristics-mix finite element method for the computation of incompressible Navier-Stokes equations with variable density. We have introduced a mixed scheme which combines a characteristics finite element scheme for treating the mass conservation equation and a finite element method to deal with the momentum equation and the divergence free constraint. The proposed me...

A simple technique is given in this paper for the construction and analysis of a class of finite element discretizations for convection-diffusion problems in any spatial dimension by properly averaging the PDE coefficients on element edges. The resulting finite element stiffness matrix is an M -matrix under some mild assumption for the underlying (generally unstructured) finite element grids. A...

We study the dispersion and dissipation of the numerical scheme obtained by taking a weighted averaging of the consistent (finite element) mass matrix and lumped (spectral element) mass matrix for the small wavenumber limit. We find and prove that for the optimum blending the resulting scheme (a) provides 2p+4 order accuracy for p-th order method (two orders more accurate compared with finite a...

saccharomyces cerevisiae (baker’s yeast) can exhibit sustained oscillations during the operation in a continuous bioreactor that adversely affects its stability and productivity. because of heterogeneous nature of cell populations, the cell population balance equation (pbe) can be used to capture the dynamic behavior of such cultures. in this work, an unstructured-segregated model is used for d...

This paper examines formulation of the discretization schemes for diffusion process simulation that allow coarse grid spacings in the areas of exponentially varying concentrations and fluxes. The method of integral identities is used as a common framework for exponential fitting of both the finite difference and finite element schemes. An exponentially fitted finite difference scheme, with disc...

We present a finite element analogue to the second-order, finite difference scheme for the solution of the heat diffusion equation in strongly magnetised plasmas given in Günter et al. [S. Günter et al., J. Comp. Phys. 209 (2005) 354]. Compared to standard finite element or finite difference formulations it strongly reduces the pollution of perpendicular heat fluxes by parallel ones even withou...