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{{see also|Patch test (medicine)}}
The '''patch test''' in the [[finite element method]] is a simple indicator of the quality of a finite element, developed by [[Bruce Irons (engineer)|Bruce Irons]].
The patch test uses a [[partial differential equation]] 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 constant [[Strain (materials science)|strain]] solution). The elements pass the patch test if the finite element solution is the same as the exact solution.<ref>{{cite book|last=Zienkiewicz |first=O. C.|authorlink=Olgierd Zienkiewicz|coauthors=R. L. Taylor, J. Z. Zhu|title=The Finite Element Method: Its Basis and Fundamentals|publisher=[[Butterworth-Heinemann]]|date=May 2005|edition=6|isbn=0750663200|accessdate=2009-08-09|language=English}}</ref>
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.<ref>{{cite book|last=Bathe|first=Klaus-Jürgen|authorlink=Klaus-Jürgen Bathe|coauthors=|title=Finite Element Procedures|publisher=[[Prentice Hall]]|date=June 1995|edition=2|isbn=097900490X|accessdate=2009-08-09|language=English}}</ref>
==References==
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