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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 863125, 19 pages
Constrained Finite Element Methods for Biharmonic Problem
College of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang 325035, China
Received 12 September 2012; Revised 29 November 2012; Accepted 29 November 2012
Academic Editor: Allan Peterson
Copyright © 2012 Rong An and Xuehai Huang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- 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.
- G. A. Baker, “Finite element methods for elliptic equations using nonconforming elements,” Mathematics of Computation, vol. 31, no. 137, pp. 45–59, 1977.
- 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.
- 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.
- 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.
- 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.
- 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.
- S. C. Brenner and L.-Y. Sung, “ interior penalty methods for fourth order elliptic boundary value problems on polygonal domains,” Journal of Scientific Computing, vol. 22-23, pp. 83–118, 2005.
- 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.
- P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland Publishing, Amsterdam, The Netherlands, 1978, Studies in Mathematics and Its Applications.
- J. Guzmán and M. Neilan, “Conforming and divergence free stokes elements on general triangular meshes,” Mathematics of Computation. In press.