Advances in Numerical Analysis
Volume 2011 (2011), Article ID 164581, 24 pages
http://dx.doi.org/10.1155/2011/164581
Research Article

Analysis and Finite Element Approximation of a Nonlinear Stationary Stokes Problem Arising in Glaciology

Guillaume Jouvet1,2 and Jacques Rappaz2

1Department of Mathematics and Computer Science, Free University of Berlin, 14195 Berlin, Germany
2Chair of Numerical Analysis and Simulation, EPFL, 1015 Lausanne, Switzerland

Received 13 September 2011; Accepted 25 October 2011

Academic Editor: Michele Benzi

Copyright © 2011 Guillaume Jouvet and Jacques Rappaz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The aim of this paper is to study a nonlinear stationary Stokes problem with mixed boundary conditions that describes the ice velocity and pressure fields of grounded glaciers under Glen's flow law. Using convex analysis arguments, we prove the existence and the uniqueness of a weak solution. A finite element method is applied with approximation spaces that satisfy the inf-sup condition, and a priori error estimates are established by using a quasinorm technique. Several algorithms (including Newton's method) are proposed to solve the nonlinearity of the Stokes problem and are proved to be convergent. Our results are supported by numerical convergence studies.