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On the finite element approximation of a semicoercive Stokes variational inequality arising in glaciology

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 نشر من قبل Gonzalo G. de Diego
 تاريخ النشر 2021
  مجال البحث الهندسة المعلوماتية
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Stokes variational inequalities arise in the formulation of glaciological problems involving contact. Two important examples of such problems are that of the grounding line of a marine ice sheet and the evolution of a subglacial cavity. In general, rigid modes are present in the velocity space, rendering the variational inequality semicoercive. In this work, we consider a mixed formulation of this variational inequality involving a Lagrange multiplier and provide an analysis of its finite element approximation. Error estimates in the presence of rigid modes are obtained by means of a novel technique involving metric projections onto closed convex cones. Numerical results are reported to validate the error estimates and demonstrate the advantages of using a mixed formulation in a glaciological application.



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