The paper presents a convergence analysis of a multigrid solver for a system of linear algebraic equations resulting from the disretization of a convection-diffusion problem using a finite element method. We consider piecewise linear finite elements in combination with a streamline diffusion stabilization . We analyze a multigrid method that is based on canonical inter-grid transfer operators, ...

We analyse the performance of the enhanced residual–free bubble (RFBe) method for the solution of convection–dominated convection–diffusion problems in 2–D, and compare the present method with the standard residual–free bubble (RFB) method. The advantages of the RFBe method are two folded: it has better stability properties and it can be used to resolve boundary layers with high accuracy on glo...

In this paper we analyze discretization of optimal control problems governed by convection-diffusion equations which are subject to pointwise control constraints. We present a stabilization scheme which leads to improved approximate solutions even on corse meshes in the convection dominated case. Moreover, the in general different approaches “optimize-then-discretize” and “discretize-then-optim...

Abstract. In this paper, we study the local discontinuous Galerkin (LDG) methods for nonlinear, time-dependent convection-diffusion systems. These methods are an extension of the Runge–Kutta discontinuous Galerkin (RKDG) methods for purely hyperbolic systems to convection-diffusion systems and share with those methods their high parallelizability, high-order formal accuracy, and easy handling o...

Standard error estimates for nite element approximations of nonstationary convection-diiusion problems depend reciprocally on the diffusion parameter ". Therefore, the estimates become worthless in the case of strong convection-dominance 0 < " 1. This work provides an "-uniform convergence theory for nite element discretizations of convection-dominated diiusion problems in Eulerian and Lagrangi...

The aim of this article is to shows that hierarchical matrices (H-matrices) provide a means to efficiently precondition linear systems arising from the streamline diffusion finite-element method applied to convection-dominated problems. Approximate inverses and approximate LU decompositions can be computed with logarithmic-linear complexity in the standard Hmatrix format. Neither the complexity...

We derive a robust a-posteriori error estimate for hp-adaptive discontinuous Galerkin (DG) discretizations of stationary convection-diffusion equations. We consider 1-irregular meshes consisting of parallelograms. The estimate yields global upper and lower bounds of the errors measured in terms of the natural energy norm associated with the diffusion and a semi-norm associated with the convecti...

The characteristic methods are known to be very efficient for convection-diffusion problems including the Navier-Stokes equations. Convergence is established when the integrals are evaluated exactly, otherwise there are even cases where divergence has been shown to happen. The family of methods studied here applies Lagrangian convection to the gradients and the function as in Yabe[?]; the metho...

In this thesis a new multiscale method, the discontinuous Galerkin multiscale method, is proposed. The method uses localized fine scale computations to correct a global coarse scale equation and thereby takes the fine scale features into account. We show a priori error bounds for convection dominated convection-diffusion-reaction problems with variable coefficients. We present an posteriori err...

A new multigrid algorithm is constructed for the solution of linear systems of equations which arise from the discretization of elliptic PDEs. It is defined in terms of the difference scheme on the fine grid only, and no rediscretization of the PDE is required. Numerical experiments show that this algorithm gives high convergence rates for several classes ofproblems: symmetric, nonsymmetdc and ...