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

Giani, Stefano

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.

Citation

Giani, S. (2015). hp-Adaptive composite discontinuous Galerkin methods for elliptic eigenvalue problems on complicated domains. Applied Mathematics and Computation, 267, 604-617. https://doi.org/10.1016/j.amc.2015.01.031

• Journal Article Type: Article
• Publication Date: Sep 15, 2015
• Deposit Date: Oct 10, 2014
• Publicly Available Date: Oct 13, 2014
• Journal: Applied Mathematics and Computation
• Print ISSN: 0096-3003
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 267
• Pages: 604-617
• DOI: https://doi.org/10.1016/j.amc.2015.01.031
• Keywords: Multi-level method, Eigenvalue problem, hp-Adaptivity, Discontinuous Galerkin, A posteriori error estimator.