The open archive for STFC research publications

Full Record Details

Persistent URL http://purl.org/net/epubs/work/53475
Record Status Checked
Record Id 53475
Title Stopping Criteria for Adaptive Finite Element Solvers
Abstract We consider a family of practical stopping criteria for linear solvers for adaptive finite element methods for symmetric elliptic problems. A contraction property between two consecutive levels of refinement of the adaptive algorithm is shown when a family of smallness criteria for the corresponding linear solver residuals are assumed on each level or refinement. More importantly, based on known and new results for the estimation of the residuals of the conjugate gradient method, we show that the smallness criteria give rise to practical stopping criteria for the iterations of the linear solver, which guarantees that the (inexact) adaptive algorithm converges. A series of numerical experiments highlights the practicality of the theoretical developments.
Organisation CSE-NAG , STFC , SCI-COMP
Keywords stopping criteria , Adaptative finite-element method , Engineering , Conjugate gradient method
Funding Information
Related Research Object(s):
Licence Information:
Language English (EN)
Type Details URI(s) Local file(s) Year
Journal Article SIAM J Sci Comput (2013). iAFEM6final.pdf 2013
Journal Article SIAM J. SCI. COMPUT. doi:10.1137/120867421 2013