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Abstract A local interpolation method for an irregular mesh of nodal points is proposed. The method is based on a Taylor expansion of the unknown function combined with the minimization of errors. Some numerical tests as well as a computer program are presented. Applicability and stability of the method are shown. By the appropirate definition of weighting coefficients, this method may be viewed as an interpolation or approximation in the sense of minimum deviation from given values. Applications in finite element and finite difference methods are shown.
Tadeusz Liszka (Sat,) studied this question.