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1999-23

A posteriori error estimation for singularly perturbed boundary value problems

by Iben, U., Warnecke, G..


Series: 1999-23, Preprints

MSC:
65N15 Error bounds
65N30 Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods
65J15 Equations with nonlinear operators (do not use [[65Hxx|65Hxx]])

Abstract:
We derive a new a posteriori error estimator for the
singularly perturbed boundary value problem associated with
convection-diffusion equations. The residual of the error
is estimated from below and above using properties of the
Galerkin-least-sqares finite element method.
The upper estimation is robust, the lower bounds depend on
the perturbation parameter.
The estimator leads to a good accuracy of the solution in
the convection dominated regions due to a sharper resolution
of the boundary layer.

Keywords:
Linear elliptic boundary value problems, a posteriori estimates, grid refinement, finite elements, convection-diffusion equation, singular perturbation