- The purpose of this paper is to present a local support-operators diffusion discretization for arbitrary 3-D hexahedral meshes.
- We use the standard finite-element definition for hexahedra [1].
- The method that we present is a generalization of a similar scheme for 2-D
*r*-*z*quadrilateral meshes that was developed by Morel, Roberts, and Shashkov [2]. - We assume a logically-rectangular mesh in our derivation for convenience, but the scheme can also be applied to unstructured meshes.
- The diffusion equation that we seek to solve can be expressed in the following general form:
- *D*=*Q*,*t*denotes the time variable, denotes a scalar function that we refer to as the intensity,*D*denotes the diffusion coefficient, and*Q*denotes the source or driving function. It is sometimes useful to express this equation in terms of a vector function, , that we refer to as the flux:= -*D*.