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Mixed methods and lower eigenvalue bounds
Published 9 Jan 2024 in math.NA and cs.NA | (2401.04519v1)
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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