ESAIM: Mathematical Modelling and Numerical Analysis

Table of Contents - September 2004 - Volume 38 - Issue05

Research Article

Finite element approximations of a glaciology problem

Chow, Sum S.a1, Carey, Graham F.a2 and Anderson, Michael L.a2

a1 Department of Mathematics, Brigham Young University, Provo, UT 84602, USA. schow@math.byu.edu.

a2 ICES, Univ. of Texas at Austin, Austin, TX 78712, USA. carey@cfdlab.ae.utexas.edu.; michaela@rsp.com.au.

Abstract

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)

Key Words:

  • Glen's flow law;
  • non-Newtonian fluids;
  • finite element error estimates;
  • successive approximations.

Mathematics Subject Classification:

  • 26B25;
  • 35J20;
  • 35J60;
  • 49J45;
  • 65N30;
  • 86A40
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