Jose E. Castillo
Computational Science Research Center
San Diego State University

"High Order Mimetic Schemes Including Boundary Conditions"

Abstract

One dimensional, higher-order finite-difference approximations of the derivative are constructed which satisfy a global conservation law. Here we present techniques that allow the construction of discrete versions of the divergence and gradient operator that have high order approximation at the boundary. We show a test problem with Robin Boundary Conditions to illustrate our schemes. This is a crucial preliminary step in creating higher-order approximations of the divergence and gradient for nonuniform grids in higher dimensions.