Summary
Standard finite element schemes applied to boundary value problems on domains with reentrant corners suffer from a global loss of accuracy caused by the influence of the corner singularities. For a model situation, it is shown that this pollution effect can be completely described in terms of an asymptotic error expansion with respect to fractional powers of the mesh size parameter. This provides the basis of an extrapolation procedure which recovers the full order of accuracy for the solution as well as for the corresponding stress intensity factors.
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Blum, H., Rannacher, R. Extrapolation techniques for reducing the pollution effect or reentrant corners in the finite element method. Numer. Math. 52, 539–564 (1987). https://doi.org/10.1007/BF01400891
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DOI: https://doi.org/10.1007/BF01400891