Patch test

from Wikipedia, the free encyclopedia

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

The patch test uses an area made up of several elements, which is structured in such a way that the exact solution is known. Typically, the exact solution to a mechanical problem consists of displacements that obey linear functions (a so-called solution with constant deformations). The elements pass the patch test if the FE solution and the analytical solution are exactly the same.

The patch test is neither sufficient nor necessary for the convergence of the finite elements. This means that even if the patch test is passed, there is no guarantee that the solution using the FE method will converge to the exact solution of the partial differential equation. Even if the FE mesh is continually refined with more elements. Conversely, failing the test does not provide any information about whether the FE solution converges to the exact solution.

literature

  • Olgierd Cecil Zienkiewicz: Finite Element Method . 2nd Edition. Hanser, 1984, ISBN 978-3-446-12525-4 (Chapters 2.7 and 11.2).
  • Klaus Jürgen Bathe: Finite Element Methods . 2., completely rework. u. exp. Edition. Springer, Berlin / Heidelberg 2001, ISBN 3-540-66806-3 .
  • OC Zienkiewicz, RL Taylor: The finite element patch test revisited a computer test for convergence, validation and error estimates . In: Computer Methods in Applied Mechanics and Engineering . tape 149 , no. 1-4 , 1997, pp. 223-254 , doi : 10.1016 / S0045-7825 (97) 00085-6 .

Web links

  • The Patch Test . Advanced Finite Element Methods for Solids, Plates and Shells (ASEN 6367) - Spring 2011 Aerospace Engineering Sciences - University of Colorado at Boulder (PDF file; 131 kB)