Anisotropic interpolation error estimates via orthogonal expansions

• Autorzy: Mingxia Li , Shipeng Mao
• Języki publikacji: EN

Abstrakty

EN

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

EN

Error estimates; Anisotropic interpolation; Orthogonal expansions

Kategorie tematyczne

• 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
• 65N15: Error bounds
• 65N50: Mesh generation and refinement
• 65N12: Stability and convergence of numerical methods

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 4
• Strony: 621-629

Daty

wydano

2013-04-01

online

2013-01-29

Twórcy

autor

Mingxia Li

• China University of Geoscience (Beijing),

autor

Shipeng Mao

• Chinese Academy of Sciences,

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

Identyfikatory

DOI

10.2478/s11533-013-0203-2