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Finite element approximations of a glaciology problem. (English) Zbl 1130.86300
Summary: We study a model problem describing the movement of a glacier under Glen’s flow law and investigated by J. Colinge and J. Rappaz [ M2AN, Math. Model. Numer. Anal. 33, No. 2, 395–406 (1999; Zbl 0946.65115)]. We establish error estimates for finite element approximation using the results of S. Chow [SIAM J. Numer. Anal. 29, No. 3, 769–780 (1992; Zbl 0749.76040)] and W. B. Liu and J. W. Barrett [SIAM J. Numer. Anal. 33, No. 1, 88–106 (1996; Zbl 0846.65064)] and give an analysis of the convergence of the successive approximations used in [Colinge and Rappaz (loc. cit.)]. 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.

MSC:
86-08 Computational methods for problems pertaining to geophysics
86A40 Glaciology
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
76A99 Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena
Software:
deal.ii
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References:
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