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Special Types of Badly Conditioned Operator Problems in Energy Spaces and Numerical Methods for Them

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Numerical Analysis and Its Applications (NAA 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1988))

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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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References

  1. Kantorovich, L. V., Akilov, G. P.: Functional Analysis in Normed Spaces, Pergamon, London, 1964.

    Google Scholar 

  2. Krein, S. G.: Linear Differential Equations in Banach Spaces, Nauka, Moscow, 1971 (in Russian).

    Google Scholar 

  3. D’yakonov, E. G.: Optimization in Solving Elliptic Problems. CRC Press, Boca Raton, 1996.

    Google Scholar 

  4. Girault, V., Raviart, P. A.: Finite Element Methods for Navier-Stokes Equations. Theory and Algorithms, Springer, Berlin, 1986.

    Google Scholar 

  5. D’yakonov, E. G.: Estimates of computational work for boundary value problems with the Stokes operators. Soviet Math. (Iz. VUZ). 27 (1983) 57–71.

    Google Scholar 

  6. Besov, O. V., Il’in, V. P., Nikol’skii, S. M.: Integral Representation of Functions and Embedding Theorems. 1 Winston and Sons, Washington, 1978; 2 A H alsted Press Book, John Wiley, New York, 1979.

    Google Scholar 

  7. D’yakonov, E. G.: Improved correctness of Stokes and Navie-Stokes type problems and their grid approximations. Vestn. Mosk. Gos. Univ., Ser.15: Vychisl. Mat. Kibern. 1998N.1 3-9.

    Google Scholar 

  8. D’yakonov, E. G.: Operator problems in strengthened Sobolev spaces and numerical methods for them. Lecture Notes in Computer Science, 1196 (1997) 161–169.

    Google Scholar 

  9. D’yakonov, E. G.: Strengthened and weakened energy spaces and their applications. Journal of Computational, Civil and Structural Engineering. 1 (2000) N. 1 42–63.

    Google Scholar 

  10. D’yakonov, E. G.: New types of a posteriori error estimates in the solution of elliptic boundary and spectral problems. Vestn. Mosk. Gos. Univ., Ser.15: Vychisl. Mat. Kibern. 1998N.4 3–9.

    Google Scholar 

  11. D’yakonov, E. G.: Cutting method for multidimensional stationary problems. Vestn. Mosk. Gos. Univ., Ser.15: Vychisl. Mat. Kibern. 1999 N.2 9-16.

    Google Scholar 

  12. Bakhvalov, N. S.: Efficint iterative methods for sti. multidimensional multiparametric problems. Comp. Math. and Math. Phys. 39 (1999) 1938–1966.

    MATH  MathSciNet  Google Scholar 

  13. Graham, I. G., Hagger, M. J.: Unstructured additive Schwarz-conjugate gradient method for elliptic problems with highly discontinuous coefficients. SIAM J. Sci. Comput. 20 (1999) 2041–2066.

    Article  MATH  MathSciNet  Google Scholar 

  14. D’yakonov, E. G.: Elliptic problems with large jumps in coefficients and asymptotically optimal algorithms for their approximate solution. Vestn. Mosk. Gos. Univ., Ser.15: Vychisl. Mat. Kibern. 2000 N.1 5-13.

    Google Scholar 

  15. D’yakonov, E. G.: On the triangulations in the finite element and efficient iterative methods. Topics in Numerical Analysis, III, Miller, J. J. H., Ed. (1977) Academic Press, London 103–124.

    Google Scholar 

  16. Thomee, V.: Galerkin Finite Element Methods for Parabolic Problems. Springer Series in Computational Mathematics, 25 (1997) Springer-Verlag, Berlin.

    Google Scholar 

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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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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41814-6

  • Online ISBN: 978-3-540-45262-1

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