Linear Systems Arising for Second-Order Mimetic Divergence and Gradient Discretizations

Recent investigations by Castillo and Grone have led to a new method for constructing mimetic discretizations of divergence and gradient operators. Their technique, which employs a matrix formulation to incorporate mimetic constraints, is capable of producing approximations whose order at a grid boundary is equal to that in the grids interior. In this paper, we construct a second-order mimetic discretization using Castillo and Grones approach and compare it to other second-order discretizations by applying them to an elliptic boundary value problem in one dimension. A detailed perturbation analysis is provided to offer some insight into the two discretizations yielding the best numerical results in the study.Mathematics Subject Classifications (2000) 65D25, 65M06, 65G99.This paper is an expanded version of the article 2] presented at the International Conference on Parallel and Distributed Processing Techniques and Applications held in Las Vegas, Nevada in June of 2003.