GENERALIZED KORN'S INEQUALITIES FOR PIECEWISE H1 AND H2 VECTOR FIELDS

. The purpose of this paper is to construct a new class of discrete generalized Korn's inequalities for piecewise H1 vector fields and piecewise H2 vector fields in three-dimensional space. The resulting Korn's inequalities are different from the standard Korn's inequalities, as they involve the tracefree symmetric gradient operator, in place of the usual symmetric gradient operator. It is anticipated that the new generalized Korn's inequalities will be useful for the analysis of a broad range of finite element methods, including mixed finite element methods and discontinuous Galerkin methods.