Is Your Mesh Refined Enough? Estimating Discretization Error Using GCI

The importance of estimating discretization error has been sadly neglected in the computational solid mechanics community. Quite the opposite is true in the computational fluid dynamics community where discretization error estimation is required to publish numerical results in many CFD journals, including the ASME Fluids Engineering Journal. It is suggested that if more solid mechanics types would estimate their discretization error, they would be surprised at the magnitude of the error in their solution attributable to meshing. In this paper the Grid Convergence Index is presented and applied to the simulation of a simple cantilever beam under a uniform distributed load. Estimates of the error in the beam end deflection are provided. To illustrate the effectiveness of CGI, the analytical solution for the cantilever beam is provided. However, an analytical solution is not required by GCI to estimate the discretization error.