On an h-type mesh-refinement strategy based on minimization of interpolation errors☆

Abstract An adaptive finite element method is proposed which involves an automatic mesh refinement in areas of the mesh where local errors are determined to exceed a pre-assigned limit. The estimation of local errors is based on interpolation error bounds and extraction formulas for highly accurate estimates of second derivatives. Applications to several two-dimensional model problems are discussed. The results indicate that the method can be very effective for both regular problems and problems with strong singularities.

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