Volume 26, pp. 146-160, 2007.
A BDDC algorithm for flow in porous media with a hybrid finite element discretization
Xuemin Tu
Abstract
The BDDC (balancing domain decomposition by constraints) methods have been applied successfully to solve the large sparse linear algebraic systems arising from conforming finite element discretizations of elliptic boundary value problems. In this paper, the scalar elliptic problems for flow in porous media are discretized by a hybrid finite element method which is equivalent to a nonconforming finite element method. The BDDC algorithm is extended to these problems which originate as saddle point problems. Edge/face average constraints are enforced across the interface and the same rate of convergence is obtained as in conforming cases. The condition number of the preconditioned system is estimated and numerical experiments are discussed.
Full Text (PDF) [231 KB], BibTeX
Key words
BDDC, domain decomposition, saddle point problem, condition number, hybrid finite element method
AMS subject classifications
65N30, 65N55, 65F10
Links to the cited ETNA articles
| [24] | Vol. 20 (2005), pp. 164-179 Xuemin Tu: A BDDC algorithm for a mixed formulation of flow in porous media |
ETNA articles which cite this article
| Vol. 45 (2016), pp. 354-370 Xuemin Tu and Bin Wang: A BDDC algorithm for second-order elliptic problems with hybridizable discontinuous Galerkin discretizations |
| Vol. 46 (2017), pp. 273-336 Clemens Pechstein and Clark R. Dohrmann: A unified framework for adaptive BDDC |
| Vol. 52 (2020), pp. 553-570 Xuemin Tu, Bin Wang, and Jinjin Zhang: Analysis of BDDC algorithms for Stokes problems with hybridizable discontinuous Galerkin discretizations |
| Vol. 58 (2023), pp. 66-83 Yanru Su, Xuemin Tu, and Yingxiang Xu: Robust BDDC algorithms for finite volume element methods |
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