On correctly evaluating orders of truncation error for node-centered edge-based schemes

Abstract

In this short note, we present a simple analysis to show that an observed order of truncation error on a regular grid can change, if not correctly evaluated, depending on the choice of the norm and also on the discretization scheme. For a second-order scheme, it can be first order, second order, or anywhere in between. Using the node-centered edge-based discretization as an example, we provide a guide on how to evaluate the order of truncation error correctly: one should evaluate it separately for a set of nodes, where the residual stencil is symmetric and the same at every node, and the rest of nodes.