A Comparison of Two Matrix Operator Formulations for Mimetic Divergence and Gradient Discretizations

摘要

Recent investigations by Castillo and Grone have led to a new method for constructing mimetic discretizations of the divergence and gradient operators. Their technique, which employs a matrix formulation to incorporate mimetic constraints, is capable or producing approximations whose order at an interval's boundary is comparable to that seen along the interval's interior. This improvement over other methods was achieved, in part, by the introduction of a particular weighted inner product in the matrix formulation. In this paper, we compare two second-order mimetic discretizations -one using the Support Operators method and one using Castillo and Grone's weighted inner product - applied to a one dimensional elliptic boundary value problem on a uniform staggered grid. Our results provide support for the use of a weighted inner product in mimetic discretizations.