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

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.