Constrained C0 Finite Element Methods for Biharmonic Problem

Abstract

This paper presents some constrained C0 finite element approximation methods for the biharmonic problem, which include the C0 symmetric interior penalty method, the C0 nonsymmetric interior penalty method, and the C0 nonsymmetric superpenalty method. In the finite element spaces, the C1 continuity across the interelement boundaries is obtained weakly by the constrained condition. For the C0 symmetric interior penalty method, the optimal error estimates in the broken H2 norm and in the L2 norm are derived. However, for the C0 nonsymmetric interior penalty method, the error estimate in the broken H2 norm is optimal and the error estimate in the L2 norm is suboptimal because of the lack of adjoint consistency. To obtain the optimal L2 error estimate, the C0 nonsymmetric superpenalty method is introduced and the optimal L2 error estimate is derived.