A Discrete Vector Calculus in Tensor Grids 1

Mimetic discretization methods for the numerical solution of continuum mechanics problems rely on analogs of vector calculus and differential forms identities in their derivation and analysis. Fully mimetic discretizations satisfy discrete analogs of the continuum theory results used to derive energy inequalities. Consequently, continuum arguments carry over and can be used to show that discrete problems are well-posed and discrete solutions converge. A fully mimetic discrete vector calculus on three dimensional tensor product grids is derived and its key properties proven.