Acosta, G.; Apel, Thomas; Durán, R. G.; Lombardi, A. L. Anisotropic error estimates for an interpolant defined via moments. (English) Zbl 1154.65007 Computing 82, No. 1, 1-9 (2008). Summary: An interpolant defined via moments is investigated for triangles, quadrilaterals, tetrahedra, and hexahedra and arbitrarily high polynomial degree. The elements are allowed to have diameters with different asymptotic behavior in different space directions. Anisotropic interpolation error estimates are proved. Cited in 6 Documents MSC: 65D05 Numerical interpolation 41A05 Interpolation in approximation theory 41A63 Multidimensional problems Keywords:anisotropic finite elements; interpolation error estimate PDFBibTeX XMLCite \textit{G. Acosta} et al., Computing 82, No. 1, 1--9 (2008; Zbl 1154.65007) Full Text: DOI References: [1] Apel T. (1999). Anisotropic finite elements: local estimates and applications. Teubner, Stuttgart · Zbl 0934.65121 [2] Apel T. and Dobrowolski M. (1992). Anisotropic interpolation with applications to the finite element method. Computing 47: 277–293 · Zbl 0746.65077 · doi:10.1007/BF02320197 [3] Apel, T., Matthies, G.: Non-conforming, anisotropic, rectangular finite elements of arbitrary order for the Stokes problem. SIAM J Numer Anal (forthcoming) · Zbl 1205.65307 [4] Buffa A., Costabel M. and Dauge M. (2005). Algebraic convergence for anisotropic edge elements in polyhedral domains. Numer Math 101: 29–65 · Zbl 1116.78020 · doi:10.1007/s00211-005-0607-4 [5] Girault V. and Raviart P.-A. (1986). Finite element methods for Navier–Stokes equations. Springer, Berlin · Zbl 0585.65077 [6] Lin, Q., Yan, N., Zhou, A.: A rectangle test for interpolated finite elements. In: Proc. of Sys. Scit. and Sys. Engng., Great Wall (Hong Kong), pp. 217–229, Culture Publish Co. (1991) [7] Mao, S., Shi, Z.-C.: Error estimates for triangular finite elements satisfying a weak angle condition. Sci China, Ser A (2007) [8] Stynes, M., Tobiska, L.: Using rectangular \({\mathcal{Q}}_{p}\) elements in the sdfem for a convection–diffusion problem with a boundary layer. Appl Numer Math (forthcoming) · Zbl 1154.65083 [9] Zhou A. and Li J. (1994). The full approximation accuracy for the stream function–vorticity–pressure method. Numer Math 68: 427–435 · Zbl 0823.65110 · doi:10.1007/s002110050070 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.