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Optimal error estimates of a locally one-dimensional method for the multidimensional heat equation. (English. Russian original) Zbl 0896.65059

Math. Notes 60, No. 2, 137-146 (1996); translation from Mat. Zametki 60, No. 2, 185-197 (1996).
Summary: For the multidimensional heat equation in a parallelepiped, optimal error estimates in \(L_2(Q)\) are derived. The error is of the order of \(\tau+| h|^2\) for any right-hand side \(f\in L_2(Q)\) and any initial function \(u_0\in \mathring W^1_2(\Omega)\); for appropriate classes of less regular \(f\) and \(u_0\), the error is of the order of \(((\tau+| h|^2)^\gamma)\), \(1/2\leq\gamma< 1\).

MSC:

65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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