Free Access
| Issue |
ESAIM: M2AN
Volume 45, Number 1, January-February 2011
|
|
|---|---|---|
| Page(s) | 115 - 143 | |
| DOI | https://doi.org/10.1051/m2an/2010034 | |
| Published online | 10 May 2010 | |
- D.N. Arnold, D. Boffi, R.S. Falk and L. Gastaldi, Finite element approximation on quadrilateral meshes. Comm. Num. Meth. Eng. 17 (2001) 805–812. [CrossRef] [Google Scholar]
- D.N. Arnold, D. Boffi and R.S. Falk, Approximation by quadrilateral finite elements. Math. Comp. 71 (2002) 909–922. [Google Scholar]
- D.N. Arnold, D. Boffi and R.S. Falk, Quadrilateral H(div) finite elements. SIAM J. Numer. Anal. 42 (2005) 2429–2451. [CrossRef] [MathSciNet] [Google Scholar]
- I. Babuška and A.K. Aziz, Survey lectures on the mathematical foundations of the finite element method, in The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, Proc. Sympos., Univ. Maryland, Baltimore, Md. Academic Press, New York (1972) 1–359. [Google Scholar]
- A. Bermúdez, P. Gamallo, M.R. Nogeiras and R. Rodríguez, Approximation properties of lowest-order hexahedral Raviart-Thomas elements. C. R. Acad. Sci. Paris, Sér. I 340 (2005) 687–692. [Google Scholar]
- S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods. Springer, New York (1994). [Google Scholar]
- F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer, New York (1991). [Google Scholar]
- F. Dubois, Discrete vector potential representation of a divergence free vector field in three dimensional domains: Numerical analysis of a model problem. SINUM 27 (1990) 1103–1142. [Google Scholar]
- T. Dupont and R. Scott, Polynomial Approximation of Functions in Sobolev Spaces. Math. Comp. 34 (1980) 441–463. [Google Scholar]
- P. Gatto, Elementi finiti su mesh di esaedri distorti per l'approssimazione di H(div) [Approximation of H(div) via finite elements over meshes of distorted hexahedra]. Master's Thesis, Dipartimento di Matematica, Università Pavia, Italy (2006). [Google Scholar]
- V. Girault and P.-A. Raviart, Finite Element Methods for Navier-Stokes Equations, Springer Series in Computational Mathematics 5. Springer-Verlag, Berlin (1986). [Google Scholar]
- R.L. Naff, T.F. Russell and J.D. Wilson, Shape Functions for Velocity Interpolation in General Hexahedral Cells. Comput. Geosci. 6 (2002) 285–314. [Google Scholar]
- T.F. Russell, C.I. Heberton, L.F. Konikow and G.Z. Hornberger, A finite-volume ELLAM for three-dimensional solute-transport modeling. Ground Water 41 (2003) 258–272. [CrossRef] [PubMed] [Google Scholar]
- P. Šolín, K. Segeth and I. Doležel, Higher Order Finite Elements Methods, Studies in Advanced Mathematics. Chapman & Hall/CRC, Boca Raton (2004). [Google Scholar]
- S. Zhang, On the nested refinement of quadrilateral and hexahedral finite elements and the affine approximation. Numer. Math. 98 (2004) 559–579. [MathSciNet] [Google Scholar]
- S. Zhang, Invertible Jacobian for hexahedral finite elements. Part 1. Bijectivity. Preprint available at http://www.math.udel.edu/ szhang/research/p/bijective1.ps (2005). [Google Scholar]
- S. Zhang, Invertible Jacobian for hexahedral finite elements. Part 2. Global positivity. Preprint available at http://www.math.udel.edu/ szhang/research/p/bijective2.ps (2005). [Google Scholar]
- S. Zhang, Subtetrahedral test for the positive Jacobian of hexahedral elements. Preprint available at http://www.math.udel.edu/ szhang/research/p/subtettest.pdf (2005). [Google Scholar]
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