EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 42 / No 2 (March-April 2008) ESAIM: M2AN, 42 2 (2008) 175-192 References
Free Access

This article has an erratum: [https://doi.org/10.1051/m2an/2020066]

Issue
ESAIM: M2AN
Volume 42, Number 2, March-April 2008
Page(s) 175 - 192
DOI https://doi.org/10.1051/m2an:2008002
Published online 27 March 2008
  1. D.N. Arnold and J. Qin, Quadratic velocity/linear pressure Stokes elements, in Advances in Computer Methods for Partial Differential Equations VII, R. Vichnevetsky and R.S. Steplemen Eds. (1992). [Google Scholar]
  2. L.J. Billera, Homology of smooth splines: generic triangulations and a conjecture of Strang. Trans. AMS 310 (1988) 325–340. [CrossRef] [Google Scholar]
  3. J.H. Bramble and X. Zhang, Multigrid methods for the biharmonic problem discretized by conforming C1 finite elements on nonnested meshes. Numer. Functional Anal. Opt. 16 (1995) 835–846. [CrossRef] [Google Scholar]
  4. S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods. Springer-Verlag, New York (1994). [Google Scholar]
  5. F. Brezzi and M. Fortin, Mixed and hybrid finite element methods. Springer (1991). [Google Scholar]
  6. P.G. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam (1978). [Google Scholar]
  7. P. Clément, Approximation by finite element functions using local regularization. RAIRO Anal. Numér. R-2 (1975) 77–84. [Google Scholar]
  8. P. Grisvard, Elliptic Problems in Nonsmooth Domains. Pitman Pub. Inc. (1985). [Google Scholar]
  9. T. Hangelbroek, G. Nürnberger, C. Rössl, H.-P. Seidel and F. Zeilfelder, Dimension of C1-splines on type-6 tetrahedral partitions. J. Approx. Theory 131 (2004) 157–184. [MathSciNet] [Google Scholar]
  10. G. Heindl, Interpolation and approximation by piecewise quadratic C1-functions of two variables, in Multivariate Approximation Theory, W. Schempp and K. Zeller Eds., Birkhäuser, Basel (1979) 146–161. [Google Scholar]
  11. M.-J. Lai, Scattered data interpolation and approximation using bivariate C1 piecewise cubic polynomials. Comput. Aided Geom. Design 13 (1996) 81–88. [CrossRef] [MathSciNet] [Google Scholar]
  12. H. Liu, D. Hong and D.-Q. Cao, Bivariate C1 cubic spline space over a nonuniform type-2 triangulation and its subspaces with boundary conditions. Comput. Math. Appl. 49 (2005) 1853–1865. [CrossRef] [MathSciNet] [Google Scholar]
  13. J. Morgan and L.R. Scott, A nodal basis for C1 piecewise polynomials of degree n. Math. Comp. 29 (1975) 736–740. [Google Scholar]
  14. J. Morgan and L.R. Scott, The dimension of the space of C1 piecewise-polynomials. Research Report UH/MD 78, Dept. Math., Univ. Houston, USA (1990). [Google Scholar]
  15. G. Nürnberger and F. Zeilfelder, Developments in bivariate spline interpolation. J. Comput. Appl. Math. 121 (2000) 125–152. [CrossRef] [MathSciNet] [Google Scholar]
  16. G. Nürnberger, C. Rössl, H.-P. Seidel and F. Zeilfelder, Quasi-interpolation by quadratic piecewise polynomials in three variables. Comput. Aided Geom. Design 22 (2005) 221–249. [CrossRef] [MathSciNet] [Google Scholar]
  17. G. Nürnberger, V. Rayevskaya, L.L. Schumaker and F. Zeilfelder, Local Lagrange interpolation with bivariate splines of arbitrary smoothness. Constr. Approx. 23 (2006) 33–59. [CrossRef] [MathSciNet] [Google Scholar]
  18. P. Oswald, Hierarchical conforming finite element methods for the biharmonic equation. SIAM J. Numer. Anal. 29 (1992) 1610–1625. [CrossRef] [MathSciNet] [Google Scholar]
  19. M.J.D. Powell, Piecewise quadratic surface fitting for contour plotting, in Software for Numerical Mathematics, D.J. Evans Ed., Academic Press, New York (1976) 253–2271. [Google Scholar]
  20. M.J.D. Powell and M.A. Sabin, Piecewise quadratic approximations on triangles. ACM Trans. on Math. Software 3 (1977) 316–325. [Google Scholar]
  21. J. Qin On the convergence of some low order mixed finite elements for incompressible fluids. Ph.D. thesis, Pennsylvania State University, USA (1994). [Google Scholar]
  22. J. Qin and S. Zhang, Stability and approximability of the P1-P0 element for Stokes equations. Int. J. Numer. Meth. Fluids 54 (2007) 497–515. [CrossRef] [Google Scholar]
  23. P.A. Raviart and V. Girault, Finite element methods for Navier-Stokes equations. Springer (1986). [Google Scholar]
  24. L.L. Schumaker and T. Sorokina, A trivariate box macroelement. Constr. Approx. 21 (2005) 413–431. [CrossRef] [MathSciNet] [Google Scholar]
  25. L.R. Scott and S. Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math. Comp. 54 (1990) 483–493. [Google Scholar]
  26. T. Sorokina and F. Zeilfelder, Optimal quasi-interpolation by quadratic C1-splines on type-2 triangulations, in Approximation Theory XI: Gatlinburg 2004, C.K. Chui, M. Neamtu and L.L. Schumaker Eds., Nashboro Press, Brentwood, TN (2004) 423–438. [Google Scholar]
  27. G. Strang, Piecewise polynomials and the finite element method. Bull. AMS 79 (1973) 1128–1137. [CrossRef] [Google Scholar]
  28. G. Strang, The dimension of piecewise polynomials, and one-sided approximation, in Conf. on Numerical Solution of Differential Equations, Lecture Notes in Mathematics 363, G.A. Watson Ed., Springer-Verlag, Berlin (1974) 144–152. [Google Scholar]
  29. M. Wang and J. Xu, Nonconforming tetrahedral finite elements for fourth order elliptic equations. Math. Comp. 76 (2007) 1–18. [Google Scholar]
  30. M. Wang and J. Xu, The Morley element for fourth order elliptic equations in any dimensions. Numer. Math. 103 (2006) 155–169. [CrossRef] [MathSciNet] [Google Scholar]
  31. S. Zhang, An optimal order multigrid method for biharmonic C1 finite element equations. Numer. Math. 56 (1989) 613–624. [CrossRef] [MathSciNet] [Google Scholar]
  32. X. Zhang, Personal communication. University of Maryland, USA (1990). [Google Scholar]
  33. X. Zhang, Multilevel Schwarz methods for the biharmonic Dirichlet problem. SIAM J. Sci. Comput. 15 (1994) 621–644. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you