Patch test

Summary

The patch test is a numerical check of a finite element: a small patch of elements must reproduce exactly any displacement field of constant strain. Bruce Irons introduced it for elements whose trial functions are not continuous across element boundaries, where the usual convergence theory does not apply. Passing the test is a practical check of consistency, and failing it signals that the element cannot converge to the right solution in general. It is used in the finite element method in structural mechanics to validate new elements.