A simple and efficient error analysis for multi-step solution of the Navier-Stokes equations
A simple error analysis is used within the context of segregated finite element solution scheme to solve incompressible fluid flow. An error indicator is defined based on the difference between a numerical solution on an original mesh and an approximated solution on a related mesh. This error indicator is based on satisfying the steady-state momentum equations. The advantages of this error indicator are, simplicity of implementation (post-processing step), ability to show regions of high and/or low error, and as the indicator approaches zero the solution approaches convergence. Two examples are chosen for solution; first, the lid-driven cavity problem, followed by the solution of flow over a backward facing step. The solutions are compared to previously published data for validation purposes. It is shown that this rather simple error estimate, when used as a re-meshing guide, can be very effective in obtaining accurate numerical solutions. Copyright © 2002 John Wiley & Sons, Ltd.
International Journal for Numerical Methods in Fluids
Fithen, R.M. (2002), A simple and efficient error analysis for multi-step solution of the Navier–Stokes equations. International Journal for Numerical Methods in Fluids 38(6): 589-608. https://doi.org/10.1002/fld.221