AuthorsA. Budisa, W. M. Boon and X. Hu
TitleMixed-Dimensional Auxiliary Space Preconditioners
AfilliationScientific Computing
Project(s)No Simula project
StatusPublished
Publication TypeJournal Article
Year of Publication2020
JournalSIAM Journal on Scientific Computing
Volume42
Issue5
PaginationA3367 - A3396
Date Published10/2020
PublisherSIAM
ISSN1064-8275
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.

URLhttps://epubs.siam.org/doi/pdf/10.1137/19M1292618
DOI10.1137/19M1292618
Citation Key27770