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.

翻译：这些问题的两个重要例子是海洋冰盖的底线和亚冰川孔隙的演化。一般而言,速度空间存在僵化模式,使变异不平等半胁迫性形成。在这项工作中,我们考虑了这种变异不平等的混合配方,涉及拉格朗格乘数,并分析了其定点元素近似值。在存在僵化模式的情况下,通过对封闭的锥形锥体进行指标预测的新技术得出错误估计。报告的数字结果证实误差估计数,并表明在冰川应用中使用混合配方的优点。