Giani, Stefano (2015) 'Solving elliptic eigenvalue problems on polygonal meshes using discontinuous Galerkin composite finite element methods.', Applied mathematics and computation., 267 . pp. 618-631.
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.
|Keywords:||Discontinuous Galerkin, Polygonal meshes, Eigenvalue problems, A priori analysis.|
|Full text:||(AM) Accepted Manuscript|
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|Publisher Web site:||http://dx.doi.org/10.1016/j.amc.2015.01.011|
|Publisher 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/|
|Record Created:||06 Oct 2014 15:05|
|Last Modified:||01 Oct 2015 15:42|
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