Volume 42, Number 2, March-April 2008
|Page(s)||175 - 192|
|Published online||27 March 2008|
- 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).
- L.J. Billera, Homology of smooth splines: generic triangulations and a conjecture of Strang. Trans. AMS 310 (1988) 325–340. [CrossRef]
- 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]
- S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods. Springer-Verlag, New York (1994).
- F. Brezzi and M. Fortin, Mixed and hybrid finite element methods. Springer (1991).
- P.G. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam (1978).
- P. Clément, Approximation by finite element functions using local regularization. RAIRO Anal. Numér. R-2 (1975) 77–84.
- P. Grisvard, Elliptic Problems in Nonsmooth Domains. Pitman Pub. Inc. (1985).
- 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]
- 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.
- M.-J. Lai, Scattered data interpolation and approximation using bivariate C1 piecewise cubic polynomials. Comput. Aided Geom. Design 13 (1996) 81–88. [CrossRef] [MathSciNet]
- 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. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed]
- J. Morgan and L.R. Scott, A nodal basis for C1 piecewise polynomials of degree n. Math. Comp. 29 (1975) 736–740.
- 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).
- G. Nürnberger and F. Zeilfelder, Developments in bivariate spline interpolation. J. Comput. Appl. Math. 121 (2000) 125–152. [CrossRef] [MathSciNet]
- 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]
- 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]
- P. Oswald, Hierarchical conforming finite element methods for the biharmonic equation. SIAM J. Numer. Anal. 29 (1992) 1610–1625. [CrossRef] [MathSciNet]
- 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.
- M.J.D. Powell and M.A. Sabin, Piecewise quadratic approximations on triangles. ACM Trans. on Math. Software 3 (1977) 316–325. [CrossRef] [MathSciNet]
- J. Qin On the convergence of some low order mixed finite elements for incompressible fluids. Ph.D. thesis, Pennsylvania State University, USA (1994).
- 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]
- P.A. Raviart and V. Girault, Finite element methods for Navier-Stokes equations. Springer (1986).
- L.L. Schumaker and T. Sorokina, A trivariate box macroelement. Constr. Approx. 21 (2005) 413–431. [CrossRef] [MathSciNet]
- L.R. Scott and S. Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math. Comp. 54 (1990) 483–493. [CrossRef] [MathSciNet] [PubMed]
- 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.
- G. Strang, Piecewise polynomials and the finite element method. Bull. AMS 79 (1973) 1128–1137. [CrossRef]
- 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.
- M. Wang and J. Xu, Nonconforming tetrahedral finite elements for fourth order elliptic equations. Math. Comp. 76 (2007) 1–18. [CrossRef] [MathSciNet]
- M. Wang and J. Xu, The Morley element for fourth order elliptic equations in any dimensions. Numer. Math. 103 (2006) 155–169. [CrossRef] [MathSciNet]
- S. Zhang, An optimal order multigrid method for biharmonic C1 finite element equations. Numer. Math. 56 (1989) 613–624. [CrossRef] [MathSciNet]
- X. Zhang, Personal communication. University of Maryland, USA (1990).
- X. Zhang, Multilevel Schwarz methods for the biharmonic Dirichlet problem. SIAM J. Sci. Comput. 15 (1994) 621–644. [CrossRef] [MathSciNet]
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