Additive Schwarz Preconditioners for Degenerate Problems with Isotropic Coefficients

S. Beuchler ()
Additional contact information
S. Beuchler: JKU Linz, Institute of Computational Mathematics

A chapter in Numerical Mathematics and Advanced Applications, 2008, pp 143-150 from Springer

Abstract: Abstract This paper deals with the numerical solution of the degenerate elliptic boundary value problem $$-\nabla \cdot x^{\alpha}\nabla u(x,y)=f(x,y), \alpha \geq 0$$ in Ω = (0, 1)2. This boundary value problem is discretized by piecewise linear finite elements on regular Cartesian grids. The corresponding linear system of algebraic equations is solved by a preconditioned conjugate gradient method with the Bramble-Pasciak-Xu preconditioner. A uniform bound of the condition number of the preconditioned system matrix is proved for α ≠ 1. The proof makes use of another additive Schwarz splitting arising from an overlapping domain decomposition of the computational domain Ω. Some numerical experiments show the efficiency of the proposed algorithm also for general polygonal domains.

Keywords: Elliptic Problem; Precondition Conjugate Gradient; Stochastic Partial Differential Equation; Space Decomposition; Degenerate Problem (search for similar items in EconPapers)
Date: 2008
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-69777-0_16

Ordering information: This item can be ordered from
http://www.springer.com/9783540697770

DOI: 10.1007/978-3-540-69777-0_16

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().