28
Views
10
CrossRef citations to date
0
Altmetric
Original Articles

The finite volume implementation of the partial asymptotic domain decomposition

&
Pages 1397-1424 | Received 16 Jun 2008, Accepted 17 Jun 2008, Published online: 21 Sep 2010

References

  • Bakhvalov , NS . 1969 . On optimization of the methods of solution of boundary value problems with boundary layers . Zh.Vyc.Mat.i Mat.Fis.(ZVMMF) , 9 ( 4 ) : 841 – 859 .
  • Ilyin , AM . 1969 . Difference scheme for a differential equation with small parameter in the higher derivative . Mat. Zametki , 6 ( 2 ) : 237 – 248 .
  • Shishkin , GI . 1992 . Network Approximations for Singularly Perturbed Elliptic and Parabolic Problems , Ekaterinburg : Russian Academy of Sciences, Ural Department .
  • Arnold , DN and Madureira , AL . 2003 . Asymptotic estimates of hierarchical modeling . Math. Model. Meth. Appl. Sci. , 13 ( 9 ) : 1329 – 1350 .
  • Kantorovich , LV and Krylov , VI . 1958 . Approximate Methods of Higher Analysis , Groningen : Noordhoff .
  • Vogelius , M and Babuska , I . 1981 . On a dimensional reduction method. I. (The optimal selection of basis functions) . Math. Comput. , 37 ( 155 ) : 31 – 46 . II. (Some approximation-theoretic results) Math. Comput. 37(155):47–68, 1981; III. (A-posteriori error estimation and an adaptive approach) Math. Comput. 37:361–384, 1981
  • Panasenko , GP . 1998 . Method of asymptotic partial decomposition of domain . Math. Model. Meth. Appl. Sci. , 8 ( 1 ) : 139 – 156 .
  • Panasenko , GP . 2000 . Method of asymptotic partial decomposition of rod structures . Int. J. Comput., Civ. Struct. Eng. (Begel House Publ.) , 1 ( 2 ) : 57 – 70 .
  • Panasenko , GP . 2000 . Asymptotic expansion of the solution of Navier–Stokes equation in tube structure and partial asymptotic decomposition of the domain . Appl. Anal. Int. J. , 76 ( 3–4 ) : 363 – 381 .
  • Panasenko , GP . 1992 . Asymptotic solutions of the elasticity theory system of equations for lattice and skeletal structures . Math. Sb. , 183 ( 1 ) : 89 – 113 . (in Russian). English transl. by AMS in Russian Acad. Sci. Sbornik Math. 75(1):85–110, 1993
  • Quarteroni , A and Formaggia , L . 2002 . “ Mathematical modelling and numerical simulation of the cardiovascular system ” . In Modelling of Living Systems, Handbook od Numerical Analysis Series , Edited by: Ayache , N . Milan : Springer .
  • Shugrin , SM . 1987 . Coupling of one-dimensional and two-dimensional models of water flow . Water Resources , 5 : 5 – 15 . (in Russian)
  • Fontvieille , F , Panasenko , G and Pousin , J . 2007 . FEM implementation for the asymptotic partial decomposition . Appl. Anal. , 86 ( 5 ) : 519 – 536 .
  • Eymard , R , Gallouet , T and Herbin , R . 2000 . Finite Volume methods, in Handbook of Numerical Analysis , Edited by: Ciarlet , PG and Lions , JL . Vol. 7 , 713 – 1020 . Amsterdam : North Holland .
  • Nazarov , SA and Specovius-Neugebauer , M . 1997 . Approximation of unbounded domains by bounded domains. Boundary value problems for Lamé operator . St. Petersburg Math. J. , 8 ( 5 ) : 879 – 912 .
  • Evans. , LC . 1998 . Partial differential equations. Graduate studies in mathematics . Amer. Math. Soc. , Providence, RI
  • Patankar , SV . 1980 . Numerical heat transfer and fluid flow, Series in Computational Methods in Mechanics and Thermal Sciences , Edited by: Minkowycz , WJ and Sparrow , EM . London : McGraw Hill .
  • Arminjon , P , Viallon , M-C and Madrane , A . 1997 . A finite volume extension of the Lax-Friedrichs and Nessyahu–Tadmor schemes for conservation laws on unstructured grids . Int. Comp. Fluid Dynamics , 9 ( 1 ) : 1 – 22 .
  • Arminjon , P and Viallon , M-C . 1999 . Convergence of a finite volume extension of the Nessyahu–Tadmor scheme on unstructured grids for a two-dimensional linear hyperbolic equation . SIAM J. Num. Anal. , 36 ( 3 ) : 738 – 771 .
  • Panasenko , GP . 2005 . Multi-scale Modelling for Structures and Composites , Dordrecht etc. : Springer .
  • Brezis , H . 1983 . Analyse fonctionnelle: Théorie et Applications , Paris : Masson .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.