A-posteriori error analysis and adaptive finite element methods for singularly perturbed convection-diffusion equations |
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Authors: | Hans-Jü rgen Reinhardt,W. Wendland |
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Abstract: | For singularly perturbed one-dimensional convection-diffusion equations, finite element approximations are constructed based on a so-called approximate symmetrization of the given unsymmetric problem. Local a-posteriori error estimates are established with respect to an appropriate energy norm where the bounds are proved to be realistic. The local bounds, called error indicators, provide a basis for a self-adaptive mesh refinement. For a model problem numerical results are presented showing that the adaptive method detects and resolves the boundary layer. |
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