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:

where

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%. Hypothetically, wouldn't it be great if, for example, on…

A presentation here at Ruhr-Universität Bochum is quite interesting. It presented a linear Richardson Extrapolation being:

*fex = fn+ k(fm - fn)*where...*fex*is the exact solution*fm*is the solution at mesh size*m**fn*is the solution at mesh size*n**k*is what I'll call Richardson Extrapolation Factor:*k = (mα) / (mα - nα)*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%. Hypothetically, wouldn't it be great if, for example, on…