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- W2622363299 abstract "We discuss adaptive numerical methods for the solution of eigenvalue problems arising eitherfrom the finite element discretization of a partial differential equation (PDE) or from discrete finite element modeling.When a model is described by a partial differential equation, the adaptive finite element methodstarts from a coarse finite element mesh which, based on a posteriori error estimators, is adaptively refinedto obtain eigenvalue/eigenfunction approximations of prescribed accuracy. This method is well established for classes of elliptic PDEs,but is still in its infancy for more complicated PDE models.For complex technical systems, the typical approach is to directly derive finite element modelsthat are discrete in space and are combined with macroscopic models to describe certain phenomena like damping or friction.In this case one typically starts with a fine uniform mesh and computes eigenvalues and eigenfunctions usingprojection methods from numerical linear algebra that are often combined with the algebraic multilevelsubstructuring to achieve an adequate performance.These methods work well in practice but their convergence and error analysis is rather difficult.We analyze the relationship between these two extreme approaches. Both approaches have their pros and cons which are discussed in detail. Our observations are demonstrated with several numerical examples." @default.
- W2622363299 created "2017-06-15" @default.
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- W2622363299 date "2016-01-01" @default.
- W2622363299 modified "2023-10-16" @default.
- W2622363299 title "Adaptive numerical solution of eigenvalue problems arising from finite element models. AMLS vs. AFEM" @default.
- W2622363299 doi "https://doi.org/10.1090/conm/658/13127" @default.
- W2622363299 hasPublicationYear "2016" @default.
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