Finite element approximations of a glaciology problem
Department of Mathematics, Brigham Young University, Provo, UT
84602, USA. firstname.lastname@example.org.
2 ICES, Univ. of Texas at Austin, Austin, TX 78712, USA. email@example.com.; firstname.lastname@example.org.
Revised: 18 June 2004
In this paper we study a model problem describing the movement of a glacier under Glen's flow law and investigated by Colinge and Rappaz [Colinge and Rappaz, ESAIM: M2AN 33 (1999) 395–406]. We establish error estimates for finite element approximation using the results of Chow [Chow, SIAM J. Numer. Analysis 29 (1992) 769–780] and Liu and Barrett [Liu and Barrett, SIAM J. Numer. Analysis 33 (1996) 98–106] and give an analysis of the convergence of the successive approximations used in [Colinge and Rappaz, ESAIM: M2AN 33 (1999) 395–406]. Supporting numerical convergence studies are carried out and we also demonstrate the numerical performance of an a posteriori error estimator in adaptive mesh refinement computation of the problem.
Mathematics Subject Classification: 26B25 / 35J20 / 35J60 / 49J45 / 65N30 / 86A40
Key words: Glen's flow law / non-Newtonian fluids / finite element error estimates / successive approximations.
© EDP Sciences, SMAI, 2004