Patch test (finite elements): Difference between revisions

Revision as of 01:16, 17 September 2007

Revision as of 05:34, 17 September 2007

Line 1:

The '''patch test''' in the finite element method is a simple indicator of the quality of a [[finite element method|finite element]], developed by [[Bruce Irons (engineer)|Bruce Irons]].

The patch test uses ana exactpartial solutiondifferential of elasticity equationsequation on a ___domain consisting from several elements, set up so that the exact solution is known. Typically, in mechanics, the prescribed exact solution consists of displacements that vary as linear functions in space (called a specialconstant case[[Strain (materials science)|strain]] solution). The elements pass the patch test if the finite element solution is the same as the exact solution.

It was long conjectured by engineers that passing the patch test is sufficient for the convergence of the finite element, that is, to ensure that the solutions from the finite element method converge to the exact solution of the [[partial differential equation]] as the finite element mesh is refined. However, this is not the case, and the patch test is neither sufficient nor necessary for convergence.