Geodesic
Difference schemes of the finite element method of increased accuracy for solving nonstationary equations
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 2, Tome 221 (2023), pp. 115-127

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Based on the finite element method with piecewise-cubic interpolation, we construct and examine three-parameter difference schemes of increased accuracy for a second-order ordinary differential equation. Stability and convergence of difference schemes are proved and accuracy estimates are obtained. The schemes proposed are tested and compared in computing experiments.
Keywords: nonstationary equations, finite difference method, finite element method, difference scheme, stability, accuracy.
Mots-clés : convergence 
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     title = {Difference schemes of the finite element method of increased accuracy for solving nonstationary equations},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {115--127},
     publisher = {mathdoc},
     volume = {221},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2023_221_a10/}
}
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D. Utebaev; G. Kh. Utepbergenova; M. M. Kazymbetova. Difference schemes of the finite element method of increased accuracy for solving nonstationary equations. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 2, Tome 221 (2023), pp. 115-127. http://geodesic.mathdoc.fr/item/INTO_2023_221_a10/