V-cycle Multigrid Algorithms for Discontinuous Galerkin Methods on Non-nested Polytopic Meshes

In this paper we analyze the convergence properties of V -cycle multigrid algorithms for the numerical solution of the linear system of equations stemming from discontinuous Galerkin discretization of second-order elliptic partial differential equations on polytopic meshes. Here, the sequence of spa...

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Bibliographic Details
Published in:Journal of scientific computing Vol. 78; no. 1; pp. 625 - 652
Main Authors: Antonietti, P. F., Pennesi, G.
Format: Journal Article
Language:English
Published: New York Springer US 01.01.2019
Springer Nature B.V
Subjects:
Algorithms
Coarsening
Computational Mathematics and Numerical Analysis
Convergence
Elliptic functions
Galerkin method
Mathematical analysis
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Methods
Multigrid methods
Partial differential equations
Polynomials
Theoretical
Multi-level methods
Discontinuous Galerkin
65F10
Non-nested spaces
65M55
cycle
65N22
Polygonal grids
ISSN:0885-7474, 1573-7691
Online Access:Get full text
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Summary:In this paper we analyze the convergence properties of V -cycle multigrid algorithms for the numerical solution of the linear system of equations stemming from discontinuous Galerkin discretization of second-order elliptic partial differential equations on polytopic meshes. Here, the sequence of spaces that stands at the basis of the multigrid scheme is possibly non-nested and is obtained based on employing agglomeration algorithms with possible edge/face coarsening. We prove that the method converges uniformly with respect to the granularity of the grid and the polynomial approximation degree p , provided that the minimum number of smoothing steps, which depends on p , is chosen sufficiently large.
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ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-018-0783-x