An enriched subspace finite element method for convection-diffusion problems

Abstract

We consider a one-dimensional convection-diffusion boundary value problem, whose solution contains a boundary layer at the outflow boundary, and construct a finite element method for its approximation. The finite element space consists of piecewise polynomials on a uniform mesh but is enriched by a finite number of functions that represent the boundary layer behavior. We show that this method converges at the optimal rate, independently of the singular perturbation parameter, when the error is measured in the energy norm associated with the problem. Numerical results confirming the theory are also presented, which also suggest that in the case of variable coefficients, the number of enrichment functions need not be as high as the theory suggests. © 2010 Institute for Scientific Computing and Information.