Exponentially fitted hierarchical bases multigrid for the convection-diffusion equation

Marc Küther

Institute for Applied Mathematics
University of Freiburg
Hermann-Herder Str. 10
79104 Freiburg, Germany


In this paper we construct hierarchical bases for an exponentially fitted finite element discretisation of the one-dimensional stationary convection-diffusion equation. Then we prove the approximation and smoothing property of the corresponding Hierarchical Bases twogrid method. Numerical experiments shall also be given for the corresponding multigrid method.