Geodesic
Independence of interpolation error estimates by polynomials of $2k+1$ degree on angles in a triangle
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 26 (2016) no. 2, pp. 160-168

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The paper considers Birkhoff-type triangle-based interpolation of two-variable function by polynomials of $2k+1$ degree by set of two variables. Similar estimates are automatically transferred to error estimates of related finite element method. The approximation error estimates of derivatives for the given finite elements depend only on the decomposition diameter, and do not depend on triangulation angles. We show that obtained approximation error estimates for a function and its partial derivatives are unimprovable. Unimprovability is understood in a following sense: there exists a function from the given class and there exist absolute positive constants independent of triangulation such that for any nondegenerate triangle estimates from below are valid. In this work, a system of specific functions is offered for interpolation conditions. These functions allow to obtain of corresponding error estimates for definite partial derivatives.
Mots-clés : error of interpolation, triangulation
Keywords: piecewise polynomial function, finite element method. 
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     author = {V. S. Bazhenov and N. V. Latypova},
     title = {Independence of interpolation error estimates by polynomials of $2k+1$ degree on angles in a triangle},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {160--168},
     publisher = {mathdoc},
     volume = {26},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2016_26_2_a1/}
}
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V. S. Bazhenov; N. V. Latypova. Independence of interpolation error estimates by polynomials of $2k+1$ degree on angles in a triangle. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 26 (2016) no. 2, pp. 160-168. http://geodesic.mathdoc.fr/item/VUU_2016_26_2_a1/