Mixed Finite Element Analysis of Eigenvalue Problems on Curved Domains

Anahí Dello Russo; Ana E. Alonso

doi:10.1515/cmam-2013-0014

Published by De Gruyter July 16, 2013

Mixed Finite Element Analysis of Eigenvalue Problems on Curved Domains

Anahí Dello Russo and Ana E. Alonso

From the journal Computational Methods in Applied Mathematics

https://doi.org/10.1515/cmam-2013-0014

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Abstract.

In this paper we present a theoretical framework for the analysis of the numerical approximations of a particular class of eigenvalue problems by mixed/hybrid methods. More precisely, we are interested in eigenproblems which are defined over curved domains or have internal curved boundaries and which may be associated with non-compact inverse operators. To do this, we consider external domain approximations Ωh of the original domain Ω, i.e., Ωh¬⊂Ω. Sufficient conditions to ensure good convergence properties and optimal error bounds for the external approximations of the eigenfunction/eigenvalue pairs are established. Then, these results are applied to the study of the Stokes eigenvalue problem with slip boundary condition defined on a curved non-convex two-dimensional domain.

Keywords: Spectral Approximation Theory; Mixed or Hybrid Methods; Curved Domains; Stokes Eigenvalue Problem; Slip Boundary Conditions

MSC: 65N12; 65N25; 65N30

Published Online: 2013-07-16

Published in Print: 2014-01-01

Mixed Finite Element Analysis of Eigenvalue Problems on Curved Domains

Abstract.

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