Patch test (finite elements)

The patch test in the finite element method is a simple indicator of the quality of a finite element. It was designed by Bruce Irons.

The patch test using a field of a plurality of elements, which is constructed so that the exact solution is known. Typically, the exact solution to a mechanical problem from shifts that linear functions obey ( a so-called solution with constant deformation ). The elements pass the patch test when the FE solution and the analytical solution are exactly the same. That means converge.

The patch test is neither sufficient nor necessary for the convergence of the finite element. That is also when passing the patch test is not guaranteed that the solution converges to the finite element method to the exact solution of the partial differential equation. Even with an ever further refinement of the FE mesh with more elements. The other way round is a failure to pass the test does not provide information about whether the FE solution converges to the exact solution.