关键词: Bingham fluid flow, penalty, orthogonality projection, finite element

Abstract: This paper is based on tome fundamental concepts in [7], Clarke’s generalized derivatives[1], as well as Lasotra’s and Strauss’ s definitions of differential D(x) of a multivalued ’function f(x)[6]. Thereby, the generalized derivatives of a region function f(x) is defined as
D_F=∪∩{G(x)⊆B(R),∀x∈B(R);G(x)=F_x=F(x)}
The existence of the generalized derivatives of a region function F(x) is discussed; the necessary and sufficient conditions of existence of the Frechet generalized derivatives of such a function is established.

Key words: Bingham fluid flow, penalty, orthogonality projection, finite element