Solving elliptic eigenvalue problems on polygonal meshes using discontinuous Galerkin composite finite element methods

Giani, Stefano

doi:10.1016/j.amc.2015.01.011

Solving elliptic eigenvalue problems on polygonal meshes using discontinuous Galerkin composite finite element methods

Giani, Stefano

Authors

Dr Stefano Giani stefano.giani@durham.ac.uk
Associate Professor

Abstract

In this paper we introduce a discontinuous Galerkin method on polygonal meshes. This method arises from the discontinuous Galerkin composite finite element method (DGFEM) for source problems on domains with micro-structures. In the context of the present paper, the flexibility of DGFEM is applied to handle polygonal meshes. We prove the a priori convergence of the method for both eigenvalues and eigenfunctions for elliptic eigenvalue problems. Numerical experiments highlighting the performance of the proposed method for problems with discontinuous coefficients and on convex and non-convex polygonal meshes are presented.

Citation

Giani, S. (2015). Solving elliptic eigenvalue problems on polygonal meshes using discontinuous Galerkin composite finite element methods. Applied Mathematics and Computation, 267, 618-631. https://doi.org/10.1016/j.amc.2015.01.011

Journal Article Type	Article
Publication Date	Sep 15, 2015
Deposit Date	Oct 6, 2014
Publicly Available Date	Oct 6, 2014
Journal	Applied Mathematics and Computation
Print ISSN	0096-3003
Publisher	Elsevier
Peer Reviewed	Peer Reviewed
Volume	267
Pages	618-631
DOI	https://doi.org/10.1016/j.amc.2015.01.011
Keywords	Discontinuous Galerkin, Polygonal meshes, Eigenvalue problems, A priori analysis.

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http://creativecommons.org/licenses/by-nc-nd/4.0/

Copyright Statement
© 2015 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/