文章基本信息

标题：Analysis and Finite Element Approximation of a Nonlinear Stationary Stokes Problem Arising in Glaciology
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作者：Guillaume Jouvet ; Jacques Rappaz
期刊名称：Advances in Numerical Analysis
印刷版ISSN：1687-9562
电子版ISSN：1687-9570
出版年度：2011
卷号：2011
DOI：10.1155/2011/164581
出版社：Hindawi Publishing Corporation
摘要：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.