a1 Department of Mathematics, Brigham Young University, Provo, UT 84602, USA. email@example.com.
a2 ICES, Univ. of Texas at Austin, Austin, TX 78712, USA. firstname.lastname@example.org.; email@example.com.
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.
(Received April 22 2003)
(Revised June 18 2004)
(Online publication October 15 2004)
Mathematics Subject Classification: