In this paper, we define a new nonconforming finite element space on parallelepiped. Using our new nonconforming space and a vector part of Kim-Kwak mixed finite element space, we suggest a new class of higher order mixed finite volume method. We show that the mixed finite volume methods can be implemented by solving the primal problem with our new nonconforming finite element methods for the pressure variable. And we can obtain the velocity variable by local recovery technique. An optimal error analysis is given and also numerical results are presented to support our analysis.
Mixed finite volume methods, nonconforming finite element methods, mixed finite element methods, error analysis.