Mixed methods and lower eigenvalue bounds

Gallistl, Dietmar

doi:10.1090/mcom/3820

Mixed methods and lower eigenvalue bounds
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by Dietmar Gallistl;

Math. Comp. 92 (2023), 1491-1509

DOI: https://doi.org/10.1090/mcom/3820

Published electronically: February 3, 2023

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Abstract:

It is shown how mixed finite element methods for symmetric positive definite eigenvalue problems related to partial differential operators can provide guaranteed lower eigenvalue bounds. The method is based on a classical compatibility condition (inclusion of kernels) of the mixed scheme and on local constants related to compact embeddings, which are often known explicitly. Applications include scalar second-order elliptic operators, linear elasticity, and the Steklov eigenvalue problem.

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