McLeod
Mechanical
- Jan 22, 2002
- 70
A while ago, I came across a reference in Benchmark magazine about Richardson Extrapolation as a useful tool for reducing discretization error. There are quite a few online references to the method, including this one, but I haven't found any which specifically discuss how to apply it to finite element data.
How does one determine the value to use for the error order parameter (k, in the linked reference)? When I run convergence checks for three meshes (h; h/2; h/4), sometimes the results appear to asymptotically approach a given value, other times they appear to progress linearly towards a value as h->0. (And then there are the singularities which increase exponentially...)
Do most analysts guess at k based on the shape of the convergence curve, or are there rules of thumb based on element type, etc.?
How does one determine the value to use for the error order parameter (k, in the linked reference)? When I run convergence checks for three meshes (h; h/2; h/4), sometimes the results appear to asymptotically approach a given value, other times they appear to progress linearly towards a value as h->0. (And then there are the singularities which increase exponentially...)
Do most analysts guess at k based on the shape of the convergence curve, or are there rules of thumb based on element type, etc.?
