### 1999-23

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