Lattice differential operators for computational physics

Abstract

Differential operators such as gradient, curl, laplacian and divergence used in vector algebra follow certain identities and symmetries, which often is absent in their discrete counterpart. For example, the laplacian operator is rotationaly symmetric. The aim of the present work is to present a general procedure to derive second order accurate discrete operators, which are isotropic to the leading order. Furthermore, by taking advantage of isotropic nature of leading order error in discrete operator, a recursive technique is developed to increase the order of accuracy of the operator.