In a previous post , I mentioned mesh convergence study is not done as often it should. I've been reminding myself to be careful in reporting stress results using sanity checks. A nagging question persists in my mind: "How much should the mesh be refined before calling it good? Is a factor of 2 good enough?" A presentation here at Ruhr-Universität Bochum is quite interesting. It presented a linear Richardson Extrapolation being: f ex = f n + k(f m - f n ) where... f ex is the exact solution f m is the solution at mesh size m f n is the solution at mesh size n k is what I'll call Richardson Extrapolation Factor: k = (m α ) / (m α - n α ) where α=2 for linear elements and α=3 for quadratic elements. To plot this factor k relative to the reduction factor ( n/m ) in Figure 1: Figure 1: Richardson Extrapolation Factor It is interesting that for quadratic elements, with a mesh size reduction by a factor of two, the factor is 114.3%. Hypothe

and other thoughts...