Numerische Mathematik

, Volume 70, Issue 1, pp 33–44 | Cite as

The inclusion of free membrane eigenvalues

  • R. Ennenbach


We present new inclusion theorems for eigenvalues of the free membrane. These permit a computation of both sided bounds from a given approximate eigenpair \((u_*,\mu_*)\) in a simple manner. For a properly normalized test function \(u_*\), the bounds depend on the quadratic forms\(\,\int_G (\Delta u_*+\mu_*u_*)^2df\,\) and\(\,\oint_\Gamma ({\partial\over\partial n} u_*)^2ds\,\) only. We give very close eigenvalue bounds for the example of the ``L''-shaped membran consisting of three unit squares.

Mathematics Subject Classification (1991):65 N25; 35 P15 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • R. Ennenbach
    • 1
  1. 1.Lehrstuhl I f\"ur Mathematik, RWTH Aachen, Augustinerbach 2a, D-52056 Aachen, Germany DE

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