The lattice Boltzmann method (LBM) has recently become an alternative and promising computational fluid dynamics approach for simulating complex fluid flows. Despite its enormous success in many practical applications, the standard LBM is restricted to the lattice uniformity in the physical space. This is the main drawback of the standard LBM for flow problems with complex geometry. Several app...

In this paper, a Godunov scheme on moving meshes, is studied for a kind of timedependent convection-dominated equations with dynamical boundary layers. The rate of convergence in pointwise norm, which is uniform to the small diffusion parameter 2, O(N−1 +τ), is proved, where N is the number of spatial unknowns and τ the mesh size of temporal meshes. This paper is a successful try on the converg...

A numerical algorithm is presented to solve a benchmark problem proposed by Hemker (1996). The incorporates asymptotic information into the design of appropriate piecewise-uniform Shishkin meshes. Moreover, different co-ordinate systems are utilized due geometries and associated layer structures that involved in this problem. Numerical results demonstrate effectiveness algorithm.

Determination of the maximum temperature and its location is the matter of the greatest importance in many technological and scientific engineering applications. In terms of numerical calculations of the heat conduction equation by using uniform mesh increments in space, large computational cost is sometimes countered. However, adaptive grid refinement method could be computationally efficient ...

In this paper, we study the stability and accuracy of adaptive finite element methods for the convection-dominated convection-diffusion-reaction problem in the twodimension space. Through various numerical examples on a type of layer-adapted grids (Shishkin grids), we show that the mesh adaptivity driven by accuracy alone cannot stabilize the scheme in all cases. Furthermore the numerical appro...

We analyze the error of a finite element domain embedding method for elliptic equations on a domain ω with curved boundary. The domain is embedded in a rectangular domain R on which uniform mesh and linear continuous elements are employed. The numerical scheme is based on an extension of the differential equation from ω to R by regularization with a small parameter (for Neumann and Robin proble...

We analyse a streamline diiusion scheme on a special piecewise uniform mesh for a model time-dependent convection-diiusion problem. The method with piecewise linear elements is shown to be convergent, independently of the diiusion parameter, with a pointwise accuracy of almost order 5=4 outside the boundary layer and almost order 3=4 inside the boundary layer. Numerical results are also given.