Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
We prove anisotropic interpolation error estimates for quadrilateral and hexahedral elements with all possible shape function spaces, which cover the intermediate families, tensor product families and serendipity families. Moreover, we show that the anisotropic interpolation error estimates hold for derivatives of any order. This goal is accomplished by investigating an interpolation defined via orthogonal expansions.
Słowa kluczowe
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
621-629
Opis fizyczny
Daty
wydano
2013-04-01
online
2013-01-29
Twórcy
autor
- China University of Geoscience (Beijing), limx@lsec.cc.ac.cn
autor
- Chinese Academy of Sciences, maosp@lsec.cc.ac.cn
Bibliografia
- [1] Acosta G., Apel T., Durán R.G., Lombardi A.L., Anisotropic error estimates for an interpolant defined via moments, Computing, 2008, 82(1), 1–9 http://dx.doi.org/10.1007/s00607-008-0259-1
- [2] Apel T., Anisotropic Finite Elements: Local Estimates and Applications, Advances in Numerical Mathematics, Teubner, Stuttgart, 1999
- [3] Apel T., Dobrowolski M., Anisotropic interpolation with applications to the finite element method, Computing, 1992, 47(3–4), 277–293 http://dx.doi.org/10.1007/BF02320197
- [4] Brenner S.C., Scott L.R., The Mathematical Theory of Finite Element Methods, Texts Appl. Math., 15, Springer, New York, 1994
- [5] Chen S., Shi D., Zhao Y., Anisotropic interpolation and quasi-Wilson element for narrow quadrilateral meshes, IMA J. Numer. Anal., 2004, 24(1), 77–95 http://dx.doi.org/10.1093/imanum/24.1.77
- [6] Chen S., Zheng Y., Mao S., Anisotropic error bounds of Lagrange interpolation with any order in two and three dimensions, Appl. Math. Comput., 2011, 217(22), 9313–9321 http://dx.doi.org/10.1016/j.amc.2011.04.015
- [7] Ciarlet P.G., The Finite Element Method for Elliptic Problems, Stud. Math. Appl., 4, North-Holland, Amsterdam-New York-Oxford, 1978
- [8] Girault V., Raviart P.-A., Finite Element Methods for Navier-Stokes equations, Springer Ser. Comput. Math., 5, Springer, Berlin, 1986
- [9] Hannukainen A., Korotov S., Křížek M., The maximum angle condition is not necessary for convergence of the finite element method, Numer. Math., 2012, 120(1), 79–88 http://dx.doi.org/10.1007/s00211-011-0403-2
- [10] Křížek M., On semiregular families of triangulations and linear interpolation, Appl. Math., 1991, 36(3), 223–232
- [11] Luke Y.L., The Special Functions and their Approximations I, Math. Sci. Eng., 53, Academic Press, New York-London, 1969
- [12] Mao S., Shi Z., Error estimates of triangular finite elements under a weak angle condition, J. Comput. Appl. Math., 2009, 230(1), 329–331 http://dx.doi.org/10.1016/j.cam.2008.11.008
- [13] Sansone G., Orthogonal Functions, Dover, New York, 1991
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0203-2