A Hybrid Mesh Selection Strategy Based on Conditioning for Boundary Value ODE Problems

An appropriate mesh selection strategy is one of the fundamental tools in designing robust codes for differential problems, especially if the codes are required to work for difficult multi scale problems. Most of the existing codes base the mesh selection on an estimate of the error (or the residual). Our strategy, based on the estimation of two parameters characterising the conditioning of the continuous problem, as well as on an estimate of the error, not only permits us to obtain a well adapted mesh, thus reducing the cost of the code, but also provides a measure of the conditioning of both continuous and discrete problems.