ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

15. Numerical Analysis and Scientific Computing

1991 MS Classification: 65 Zaitseva, Svetlana, Moscow Power Engineering Institute (Technical University), Moscow, Russia On sharp error estimates in L_{2}-norm for methods of solving the heat equation in non-smooth data classes Various locally one-dimensional and vector splitting methods of the approximation order O(τ^{k} + h^{2}) (k = 1, 2) of solving the initial boundary value problem for the heat equation are studied. For k = 1, the optimal error estimates O(τ +h^{2}) and the derivatives error estimates O(\sqrt{τ} +h+τ/h) from above and from below are derived for right-hand side f ∈ L_{2}(Q) and the initial function u_{0} ∈ ∘^{→}W _{2}^{1}(Ω). Besides, there is the set of the estimates for less regular f, u_{0}. For k = 2, the sharp error estimates O(τ^{2} + h^{2} + τ^{2}/h^{2(1−λ)}) (λ ∈ [0, 1]) are derived for corresponding classes of f, u_{0}. Most of the estimates is inferior in order to the estimates for the implicit and Crank-Nicolson methods. These results are achieved jointly with A. A. Zlotnik and supported by the RFBR (grant 97-01-00214). References: 1. S. B. Zaitseva and A. A. Zlotnik. Math. Notes 60 (1996), 137-146. 2. S. B. Zaitseva and A. A. Zlotnik. Russ. Math. 41 (1997), 51-65. 3. S. B. Zaitseva and A. A. Zlotnik. RJNAMM 13 (1998), 69-91.