Abstract
A finite element with new properties of approximation of higher derivatives is constructed, and a method for the construction of a finite element space in the planar case is proposed. The method is based on Yu.N. Subbotin’s earlier results as well as on the results obtained in this paper. The constructed piecewise polynomial function possesses the continuity property and new approximation properties.
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P. G. Ciarlet and P. A. Raviart, “General Lagrange and Hermite interpolation in R n with applications to finite element methods,” Arch. Rational Mech. Anal. 46 (3), 177–199 (1972).
Yu. N. Subbotin, “Multidimensional piecewise continuous interpolation,” in Approximation and Interpolation Methods, Ed. by A. Yu. Kuznetsov (VTsN, Novosibirsk, 1981), pp. 148–153 [in Russian].
Yu. N. Subbotin, “The dependence of estimates of a multidimensional piecewise-polynomial approximation on the geometric characteristics of a triangulation,” Proc. Steklov Inst. Math. 4, 135–159 (1990).
N. V. Baidakova, “Influence of smoothness on the error of approximation of derivatives under local interpolation on triangulations,” Proc. Steklov Inst. Math. 277 (Suppl. 1), S33–S47 (2012).
J. Brandts, A. Hannukainen, S. Korotov, and M. Krizek, “On angle conditions in the finite element method,” SeMA J., No. 56, 81–95 (2011).
I. S. Berezin and N. P. Zhidkov, Computing Methods (Fizmatgiz, Moscow, 1962; Pergamon, Oxford, 1965), Vol. 1.
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Original Russian Text © N.V. Baidakova, 2015, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2015, Vol. 21, No. 4.
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Baidakova, N.V. A triangular finite element with new approximation properties. Proc. Steklov Inst. Math. 296 (Suppl 1), 74–84 (2017). https://doi.org/10.1134/S0081543817020079
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DOI: https://doi.org/10.1134/S0081543817020079