The penalty method for grid matching in mixed finite element methods (Q735939)

The finite element method of Hermann-Hellan-Johnson [\textit{F. Brezzi} and \textit{P. A. Raviart}, Mixed finite element methods for 4th order elliptic equations. Topics in numerical analysis III, Proc. R. Irish Acad. Conf., Dublin 1976, 33--56 (1977; Zbl 0434.65085); \textit{R. S. Falk} and \textit{J. E. Osborn}, RAIRO, Anal. Numér. 14, 249--277 (1980; Zbl 0467.65062)] for the biharmonic equation is considered for non-matching grids. Matching conditions are replaced by penalty terms. The convergence rate is less than that of the mixed finite element method on matching grids with any choice of penalty parameters. This is in contrast to results by the authors for other finite element methods.