Hybrid methods from a new perspective

Abstract

Usually, by a hybrid method it is understood one in which continuity requirements are reduced or eliminated altogether [Babuska, et al., 1977, 1978; Pian & Tong, 1969; Tong, 1970] by introducing auxiliary dependent variables. Finite element methods for elliptic equations of order 2m, are said to be nonconforming when in the evaluation of the energy, which involves derivatives of order m, the approximations to derivatives of order m-1 may have simple discontinuities [Nitsche, 1974; Strang, 1972].