We are concerned with the derivation of Poincare-Friedrichs type inequalities in the broken Sobolev space W^(2,1)(Ω;T h)with respect to a geometrically conforming,simplicial triagulation T h of a bounded Lipschitz domainΩin R d,d∈N.Such inequalities are of interest in the numerical analysis of nonconforming finite element discretizations such as C^(0) Discontinuous Galerkin(C^(0)DG)approximations of minimization problems in the Sobolev space W^(2,1)(Ω),or more generally,in the Banach space BV^(2)(Ω)of functions of bounded second order total variation.As an application,we consider a C^(0) DG approximation of a minimization problem in BV^(2)(Ω)which is useful for texture analysis and management in image restoration.
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