Abstract
Badly conditioned operator problems in Hilbert spaces are characterized by very large condition numbers. For special types of such problems, their reduction to ones with strongly saddle operators leads to remarkable improvement of correctness and to justification of the famous Bakhvalov—Kolmogorov principle about asymptotically optimal algorithms. The first goal of the present paper is to present a short review of recently obtained results for stationary problems in classical Sobolev and more general energy spaces. The second goal is a study of the approach indicated above to the case of nonstationary problems; special attention is paid to parabolic problems with large jumps in coefficients; the study is based on relatively new extension theorems and special energy methods.
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D’yakonov, E.G. (2001). Special Types of Badly Conditioned Operator Problems in Energy Spaces and Numerical Methods for Them. In: Vulkov, L., Yalamov, P., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2000. Lecture Notes in Computer Science, vol 1988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45262-1_33
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DOI: https://doi.org/10.1007/3-540-45262-1_33
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