Analysis and Finite Element Approximation of a Nonlinear Stationary Stokes Problem Arising in Glaciology. (12th January 2012)

• Record Type: Journal Article
• Authors: Jouvet, Guillaume; Rappaz, Jacques
• Other Names: Benzi Michele Academic Editor.
• Is Part Of: Advances in numerical analysis. Volume 2011(2011)
• Publication Date: 2012-01-12
• Subjects: Numerical analysis -- Periodicals; Numerical analysis; Periodicals; Electronic journals; 518
• DOI: 10.1155/2011/164581
• Languages: English
• ISSNs: 1687-9562

Abstract

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.