hp-Adaptive composite discontinuous Galerkin methods for elliptic eigenvalue problems on complicated domains

Stefano Giani

Applied Mathematics and Computation, 2015, vol. 267, issue C, 604-617

Abstract: In this paper we develop the a posteriori error estimation of hp-adaptive discontinuous Galerkin composite finite element methods (DGFEMs) for the discretization of second-order elliptic eigenvalue problems. DGFEMs allow for the approximation of problems posed on computational domains which may contain local geometric features. The dimension of the composite finite element space is independent of the number of geometric features. This is in contrast with standard finite element methods, as the minimal number of elements needed to represent the underlying domain can be very large and so the dimension of the finite element space. Computable upper bounds on the error for both eigenvalues and eigenfunctions are derived. Numerical experiments highlighting the practical application of the proposed estimators within an automatic hp-adaptive refinement procedure will be presented.

Keywords: Multi-level method; Eigenvalue problem; hp-Adaptivity; Discontinuous Galerkin; A posteriori error estimator (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:267:y:2015:i:c:p:604-617

DOI: 10.1016/j.amc.2015.01.031

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