A dual mesh finite domain method for the numerical solution of differential equations. Issue 3 (4th May 2019) - Reddy, J. N.
Abstract: A method that employs a dual mesh, one for primary variables and another for dual variables, for the numerical solution of differential equations is presented. The formulation makes use of the traditional finite element interpolation of the primary variables (primal mesh) and the subdomain concept akin to the so-called finite volume method to satisfy the integral form of the governing differential equations on a dual mesh. The approach is termed a dual-mesh finite domain method to distinguish it from both the finite element method and the finite volume method, although the method shares the desirable features of both methods. The method is introduced as applied to representative differential equations in 1-D and 2-D. Numerical examples are presented to illustrate the methodology and accuracy compared to the finite element and finite volume solutions.