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

Abstract

For the multidimensional heat equation in a parallelepiped, optimal error estimates inL2(Q) are derived. The error is of the order of τ+¦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 ((τ+¦h¦2γ), 1/2≤γ<1.