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A new method using \(C^0\)IPG for the biharmonic eigenvalue problem. (English) Zbl 1490.65257

Summary: The paper presents a new proof of the \(C^0\)IPG method \((C^0\) interior penalty Galerkin method) for the biharmonic eigenvalue problem. Instead of using the proof following the structure of discontinuous Galerkin method, we rewrite the problem as the eigenvalue problem of a holomorphic Fredholm operator function of index zero. The convergence for \(C^0\)IPG is proved using the abstract approximation theory for holomorphic operator functions. We employ the spectral indicator method which is easy in coding to compute the eigenvalues. Numerical examples are presented to validate the theory.

MSC:

65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
47B07 Linear operators defined by compactness properties
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