Диссертация (1149340), страница 22
Текст из файла (страница 22)
Adaptive multilevel solution of nonlinear parabolic PDE systems. Springer-Verlag,Berlin, 2001. Т. 16. С. xii+157.8. Braess D. Finite elements. Second изд. Cambridge: Cambridge University Press, 2001.С. xviii+352.9. Grossmann C., Roos H.-G., Stynes M. Numerical treatment of partial differential equations.Springer, Berlin, 2007. С. xii+591.10. Johnson C. Numerical solution of partial differential equations by the finite element method.Mineola, NY: Dover Publications Inc., 2009.
С. ii+279.11. Langer U., Wolfmayr M. Multiharmonic finite element analysis of a time-periodic parabolicoptimal control problem // J. Numer. Math. 2013. Т. 21, № 4. С. 265–300.12. Fourier J. B. J. Analytical theory of heat // Great Books of the Western World, no. 45.Encyclopaedia Britannica, Inc., Chicago, London, Toronto, 1952. С. 163–251.13. Carslow H.
S., Jaeger J. C. Conduction of Heat in Solids. Oxford Univ. Press (Clarendon),London and New York, 1948.14. Widder D. V. The heat equation. Academic Press [Harcourt Brace Jovanovich, Publishers],New York-London, 1975. С. xiv+267.15. Cannon J. R. The one-dimensional heat equation. Addison-Wesley Publishing Company,Advanced Book Program, Reading, MA, 1984. Т.
23. С. xxv+483.16. Black F., Scholes M. The pricing of options and corporate liabilities // Financial riskmeasurement and management. Edward Elgar, Cheltenham, 2012. Т. 267. С. 100–117.12917. Pearson K. The Problem of the Random Walk // Nature. 1905. Т. 72. С. 294, 318, 342.18.
Vázquez J. L. The porous medium equation. The Clarendon Press, Oxford University Press,Oxford, 2007. С. xxii+624.19. Сармин Э. Н., Чудов Л. А. Об устойчивости численного интегрирования систем обыкновенных дифференциальных уравнений, возникающих при применении метода прямых // Ж. вычисл. матем. и матем. физ. 1963. Т. 3, № 6. С.
1122–1125.20. Courant R. Variational methods for the solution of problems of equilibrium and vibrations //Bull. Amer. Math. Soc. 1943. Т. 49. С. 1–23.21. Zlámal M. On the finite element method // Numer. Math. 1968. Т. 12. С. 394–409.22. Ciarlet P. G. The finite element method for elliptic problems. North-Holland Publishing Co.,Amsterdam-New York-Oxford, 1978.23.
Lax A. Decaying shocks. A comparison of an approximate analytic solution with a finitedifference method // Communications on Appl. Math. 1948. Т. 1. С. 247–257.24. Morton K. W., Mayers D. F. Numerical solution of partial differential equations. CambridgeUniversity Press, Cambridge, 1994.25. Crank J. The mathematics of diffusion.Second изд.Clarendon Press, Oxford, 1975.С.
ix+414.26. Самарский А.А., Николаев Е.С. Методы решения сеточных уравнений. Москва: Наука,1978.27. Самарский А. А., Гулин А. В. Численные методы. Наука, Москва, 1989.28. Toro E. F. Riemann solvers and numerical methods for fluid dynamics. Second изд. SpringerVerlag, Berlin, 1999. С. xx+624.29. Eymard R., Gallouët T., Herbin R. Finite volume methods // Handbook of numericalanalysis, Vol. VII. North-Holland, Amsterdam, 2000. С. 713–1020.30. LeVeque R.
J. Finite volume methods for hyperbolic problems. Cambridge University Press,Cambridge, 2002. С. xx+558.31. Zafarullah A. Application of the method of lines to parabolic partial differential equationswith error estimates // J. Assoc. Comput. Mach. 1970. Т. 17. С. 294–302.32. Verwer J. G., Sanz-Serna J. M. Convergence of method of lines approximations to partialdifferential equations // Computing. 1984. Т. 33, № 3-4. С. 297–313.13033. Schiesser W. E. Computational mathematics in engineering and applied science: ODEs,DAEs, and PDEs. CRC Press, Boca Raton, FL, 1994.
С. xii+587.34. Hackbusch W. Parabolic multigrid methods // Computing methods in applied sciences andengineering, VI (Versailles, 1983). North-Holland, Amsterdam, 1984. С. 189–197.35. Womble D. E. A time-stepping algorithm for parallel computers // SIAM J.
Sci. Statist.Comput. 1990. Т. 11, № 5. С. 824–837.36. Vandewalle S., Piessens R. Efficient parallel algorithms for solving initial-boundary value andtime-periodic parabolic partial differential equations // SIAM J. Sci. Statist. Comput. 1992.Т. 13, № 6. С. 1330–1346.37. Horton G., Vandewalle S. A space-time multigrid method for parabolic partial differentialequations // SIAM J. Sci. Comput. 1995.
Т. 16, № 4. С. 848–864.38. Friedrichs K. Eine invariante Formulierung des Newtonschen Gravitationsgesetzes und desGrenzüberganges vom Einsteinschen zum Newtonschen Gesetz // Math. Ann. 1927. Т. 98.С. 566–575.39. Friedrichs K. On certain inequalities and characteristic value problems for analytic functionsand for functions of two variables // Trans. Amer.
Math. Soc. 1937. Т. 41, № 3. С. 321–364.40. Steklov V. A. On the expansion of a given function into a series of harmonic functions (inRussian) // Communs Kharkov Math. Soc. 1897. Т. 2, № 6. С. 57–124.41. Maz′ ja V. G. Sobolev spaces with applications to elliptic partial differential equations.augmented изд.
Springer, Heidelberg, 2011. Т. 342. С. xxviii+866.42. Poincare H. Sur les Equations aux Derivees Partielles de la Physique Mathematique // Amer.J. Math. 1890. Т. 12, № 3. С. 211–294.43. Poincare H. Sur les Equations de la Physique Mathematique // Rend. Circ.
Mat. Palermo.1894. Т. 8. С. 57–156.44. Филонов Н. Об одном неравенстве на собственные числа задач Дирихле и Неймана дляоператора Лапласа // Алгебра и анализ. 2004. Т. 16, № 2. С. 172–176.45. Steklov V. A. The problem of cooling of an heterogeneous rigid rod (in Russian) // CommunsKharkov Math. Soc. 1896. Т. 2, № 5. С. 136–181.46. Steklov V.
A. Probléme de refroidissement d’une barre hétérogéne // Ann. fac. sci. Toulouse.1901. Т. 2, № 3. С. 281–313.47. Mikhlin S. G. Constants in some inequalities of analysis. John Wiley and Sons, Ltd.,Chichester, 1986. С. 108.13148. Payne L. E., Weinberger H. F. An optimal Poincaré inequality for convex domains // Arch.Rational Mech. Anal. 1960. Т. 5. С. 286–292 (1960).49. Laugesen R.
S., Siudeja B. A. Minimizing Neumann fundamental tones of triangles: anoptimal Poincaré inequality // J. Differential Equations. 2010. Т. 249, № 1. С. 118–135.50. Cheng S. Y. Eigenvalue comparison theorems and its geometric applications // Math. Z.1975. Т. 143, № 3. С. 289–297.51. Laugesen R. S., Siudeja B.
A. Maximizing Neumann fundamental tones of triangles // J.Math. Phys. 2009. Т. 50, № 11. С. 112903, 18.52. Pinsky M. A. The eigenvalues of an equilateral triangle // SIAM J. Math. Anal. 1980. Т. 11,№ 5. С. 819–827.53. Hoshikawa Y., Urakawa H. Affine Weyl groups and the boundary value eigenvalue problemsof the Laplacian // Interdiscip. Inform. Sci.
2010. Т. 16, № 1. С. 93–109.54. Nakao M. T., Yamamoto N. A guaranteed bound of the optimal constant in the errorestimates for linear triangular element // Topics in numerical analysis. Springer, Vienna,2001. Т. 15. С. 165–173.55. Bérard P. H. Spectres et groupes cristallographiques. I. Domaines euclidiens // Invent.
Math.1980. Т. 58, № 2. С. 179–199.56. Steklov V. A. Sur les problémes fondamentaux de la physique mathematique // Annales sci.ENS. 1902. Т. 3, № 19. С. 191–259, 455–490.57. Fox D. W., Kuttler J. R. Sloshing frequencies // Z. Angew. Math. Phys. 1983. Т. 34, № 5.С. 668–696.58. Kozlov V., Kuznetsov N. The ice-fishing problem: the fundamental sloshing frequency versusgeometry of holes // Math. Methods Appl. Sci. 2004.
Т. 27, № 3. С. 289–312.59. Kozlov V., Kuznetsov N., Motygin O. On the two-dimensional sloshing problem // Proc. R.Soc. Lond. Ser. A Math. Phys. Eng. Sci. 2004. Т. 460, № 2049. С. 2587–2603.60. Kuznetsov N., Nazarov A. Sharp constants in the Poincaré, Steklov and related inequalities(a survey) // Mathematika. 2015. Т. 61, № 2. С.
328–344.61. Girouard A., Polterovich I. Spectral geometry of the Steklov problem // arXiv.org. 2014. Т.math/1411.6567.62. Nazarov A. I., Repin S. I. Exact constants in Poincare type inequalities for functions withzero mean boundary traces // Mathematical Methods in the Applied Sciences. John Wileyand Sons, Ltd., 2014.13263. Banach S. Sur les opérations dans les ensembles abstraits et leur application aux équationsintégrales // Fund.
Math. 1922. Т. 3. С. 133–181.64. Collatz L. Funktionan alysis und numerische Mathematik. Springer-Verlag, Berlin, 1964.65. Колмогоров А. Н., Фомин С. В. Элементы теории функций и функционального анализа.Наука, Москва, 1976.66. Istratescu V. I. Fixed Point Theory, An Introduction. The Netherlands, 1981.67.
Zeidler E. Nonlinear functional analysis and its applications. I: Fixed-point theorems.Springer-Verlag, New York, 1986.68. Brenner S., Scott R. L. The mathematical theory of finite element methods. Springer, NewYork, 1994.69. Strang G., Fix G. An analysis of the finite element method. Prentice Hall, Englewood Cliffs,1973.70. Babuška I., Rheinboldt W.
C. A-posteriori error estimates for the finite element method //Internat. J. Numer. Meth. Engrg. 1978. Т. 12. С. 1597–1615.71. Babuška I., Rheinboldt W. C. Error estimates for adaptive finite element computations //SIAM J. Numer. Anal. 1978. Т. 15, № 4. С. 736–754.72. Zienkiewicz O. C., Zhu J.















