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Mixed-dimensional auxiliary space preconditioners

Budisa, Ana; Boon, Wietse; Hu, Xiaozhe
Journal article, Peer reviewed
Published version
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URI
https://hdl.handle.net/11250/2765958
Date
2020
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  • Department of Mathematics [1038]
  • Registrations from Cristin [12804]
Original version
SIAM Review. 2020, 42 (5), A3367–A3396.   10.1137/19M1292618
Abstract
This work introduces nodal auxiliary space preconditioners for discretizations of mixed-dimensional partial differential equations. We first consider the continuous setting and generalize the regular decomposition to this setting. With the use of conforming mixed finite element spaces, we then expand these results to the discrete case and obtain a decomposition in terms of nodal Lagrange elements. In turn, nodal preconditioners are proposed analogous to the auxiliary space preconditioners of Hiptmair and Xu [SIAM J. Numer. Anal., 45 (2007), pp. 2483--2509]. Numerical experiments show the performance of this preconditioner in the context of flow in fractured porous media.
Publisher
SIAM
Journal
SIAM Review
Copyright
Copyright 2020, Society for Industrial and Applied Mathematics

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