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Optimal error estimates of a locally one-dimensional method for the multidimensional heat equation

Authors:	S. B. Zaitseva A. A. Zlotnik

Affiliation:	(1) Moscow Power Engineering Institute, USSR

Abstract:	For the multidimensional heat equation in a parallelepiped, optimal error estimates inL₂(Q) are derived. The error is of the order of +¦h¦² for any right-hand sidef L₂(Q) and any initial function $u_0 in mathop {W_2^1 }limits^ circ left( Omega right)$ ; for appropriate classes of less regularf andu₀, the error is of the order of ((+¦h¦²), 1/2<1.Translated fromMatematicheskie Zametki, Vol. 60, No. 2, pp. 185–197, August, 1996.

Keywords:	locally one-dimensional method multidimensional heat equation difference schemes optimal error methods
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