Multigrid algorithms for hp-version Interior Penalty Discontinuous Galerkin methods on polygonal and polyhedral meshes

Antonietti, P. F. and Sarti, M. and Verani, M. and Houston, P. (2014) Multigrid algorithms for hp-version Interior Penalty Discontinuous Galerkin methods on polygonal and polyhedral meshes. Numerische Mathematik . ISSN 0029-599X (Submitted)

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Abstract

In this paper we analyze the convergence properties of two-level and W-cycle multigrid solvers for the numerical solution of the linear system of equations arising from hp-version symmetric interior penalty discontinuous Galerkin discretizations of second-order elliptic partial differential equations on polygonal/polyhedral meshes. We prove that the two-level method converges uniformly with respect to the granularity of the grid and the polynomial approximation degree p, provided that the number of smoothing steps, which depends on p, is chosen sufficiently large. An analogous result is obtained for the W-cycle multigrid algorithm, which is proved to be uniformly convergent with respect to the mesh size, the polynomial approximation degree, and the number of levels, provided the latter remains bounded and the number of smoothing steps is chosen sufficiently large. Numerical experiments are presented which underpin the theoretical predictions; moreover, the proposed multilevel solvers are shown to be convergent in practice, even when some of the theoretical assumptions are not fully satisfied.

Item Type: Article
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Mathematical Sciences
Related URLs:
URLURL Type
http://link.springer.com/journal/volumesAndIssues/211Publisher
Depositing User: Houston, Paul
Date Deposited: 27 Aug 2015 08:16
Last Modified: 16 Sep 2016 07:01
URI: http://eprints.nottingham.ac.uk/id/eprint/29674

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