Constrained C0 Finite Element Methods for Biharmonic Problem. (13th December 2012)

• Record Type: Journal Article
• Authors: An, Rong; Huang, Xuehai
• Other Names: Peterson Allan Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2012(2012)
• Publication Date: 2012-12-13
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2012/863125
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : This paper presents some constrained C 0 finite element approximation methods for the biharmonic problem, which include the C 0 symmetric interior penalty method, the C 0 nonsymmetric interior penalty method, and the C 0 nonsymmetric superpenalty method. In the finite element spaces, the C 1 continuity across the interelement boundaries is obtained weakly by the constrained condition. For the C 0 symmetric interior penalty method, the optimal error estimates in the broken H 2 norm and in the L 2 norm are derived. However, for the C 0 nonsymmetric interior penalty method, the error estimate in the broken H 2 norm is optimal and the error estimate in the L 2 norm is suboptimal because of the lack of adjoint consistency. To obtain the optimal L 2 error estimate, the C 0 nonsymmetric superpenalty method is introduced and the optimal L 2 error estimate is derived.