99-23
A posteriori error estimation for singularly perturbed boundary value problems
Preprint series: 99-23, Preprints
- MSC:
- 65N15 Error bounds
- 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
- 65J15 Equations with nonlinear operators (do not use 65Hxx)
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
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