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1. D. N. Arnold, F. Brezzi, B. Cockburn, and L. D. Marini, “Unified analysis of discontinuous Galerkin methods for elliptic problems,” SIAM Journal on Numerical Analysis, vol. 39, no. 5, pp. 1749–1779, 2002. View at Publisher · View at Google Scholar
2. G. A. Baker, “Finite element methods for elliptic equations using nonconforming elements,” Mathematics of Computation, vol. 31, no. 137, pp. 45–59, 1977.
3. I. Mozolevski and E. Süli, “A priori error analysis for the hp-version of the discontinuous Galerkin finite element method for the biharmonic equation,” Computational Methods in Applied Mathematics, vol. 3, no. 4, pp. 596–607, 2003.
4. I. Mozolevski, E. Süli, and P. R. Bösing, “hp-version a priori error analysis of interior penalty discontinuous Galerkin finite element approximations to the biharmonic equation,” Journal of Scientific Computing, vol. 30, no. 3, pp. 465–491, 2007. View at Publisher · View at Google Scholar
5. E. Süli and I. Mozolevski, “hp—version interior penalty DGFEMs for the biharmonic equation,” Computer Methods in Applied Mechanics and Engineering, vol. 196, no. 13–16, pp. 1851–1863, 2007. View at Publisher · View at Google Scholar
6. I. Babuška and M. Zlámal, “Nonconforming elements in the finite element method with penalty,” SIAM Journal on Numerical Analysis, vol. 10, pp. 863–875, 1973.
7. G. Engel, K. Garikipati, T. J. R. Hughes, M. G. Larson, L. Mazzei, and R. L. Taylor, “Continuous/discontinuous finite element approximations of fourth-order elliptic problems in structural and continuum mechanics with applications to thin beams and plates, and strain gradient elasticity,” Computer Methods in Applied Mechanics and Engineering, vol. 191, no. 34, pp. 3669–3750, 2002. View at Publisher · View at Google Scholar
8. S. C. Brenner and L.-Y. Sung, “$C^0$ interior penalty methods for fourth order elliptic boundary value problems on polygonal domains,” Journal of Scientific Computing, vol. 22-23, pp. 83–118, 2005. View at Publisher · View at Google Scholar
9. B. Rivière, M. F. Wheeler, and V. Girault, “Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. I,” Computational Geosciences, vol. 3, no. 3-4, pp. 337–360, 1999. View at Publisher · View at Google Scholar
10. P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland Publishing, Amsterdam, The Netherlands, 1978, Studies in Mathematics and Its Applications.
11. J. Guzmán and M. Neilan, “Conforming and divergence free stokes elements on general triangular meshes,” Mathematics of Computation. In press.