A numerical method is presented to solve a two-dimensional hyperbolic diffusion problem where is assumed that both convection and diffusion are responsible for flow motion. Since direct solutions based on implicit schemes for multidimensional problems are computa-tionally inefficient, we apply an alternating direction method which is second order accurate in time and space. The stability of the...

A finite element method for a singularly perturbed convection-diffusion problem with exponential boundary layers is analysed. Using a mortaring technique we combine an anisotropic triangulation of the layer region (into rectangles) with a shape regular one of the remainder of the domain. This results in a possibly non-matching (and hybrid), but layer adapted mesh of Shishkin type. We study the ...

In this paper we consider singularly perturbed ordinary differential equations with convection terms. An ε-uniformly convergent finite difference scheme is constructed for such boundary value problems by using an upwind finite difference operator and a piecewise uniform mesh. Our primary interest is the design of a numerical method, for which a parallel technique will later be applicable. In th...

For the solution of convection-diffusion problems we present a multilevel self-adaptive mesh-refinement algorithm to resolve locally strong varying behavior, like boundary and interior layers. The method is based on discontinuous Galerkin (Baumann-Oden DG) discretization. The recursive mesh-adaptation is interwoven with the multigrid solver. The solver is based on multigrid V-cycles with damped...

We experimentally examine the performance of preconditioners based on entries of the symmetric positive definite part and small subspace solvers for linear system of equations obtained from the high-order compact discretization of convection-diffusion equations. Numerical results are described to illustrate that the preconditioned GMRES algorithm converges in a reasonable number of iterations.

A functional type a posteriori error estimator for the finite element discretisation of the stationary reaction-convection-diffusion equation is derived. In case of dominant convection, the solution for this class of problems typically exhibits boundary layers and shock-front like areas with steep gradients. This renders the accurate numerical solution very demanding and appropriate techniques ...

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 paper, we consider the adaptive Eulerian–Lagrangian method (ELM) for linear convection-diffusion problems. Unlike the classical a posteriori error estimations, we estimate the temporal error along the characteristics and derive a new a posteriori error bound for ELM semi-discretization. With the help of this proposed error bound, we are able to show the optimal convergence rate of ELM f...

We consider the numerical approximation of a model convection–diffusion equation by standard bilinear finite elements. Using appropriately graded meshes we prove optimal order error estimates in the ε-weighted H 1-norm valid uniformly, up to a logarithmic factor, in the singular perturbation parameter. Finally, we present some numerical examples showing the good behavior of our method. © 2006 I...