  Stokes variational inequalities arise in the formulation of glaciological
problems involving contact. We consider the problem of a two-dimensional marine
ice sheet with a grounding line, although the analysis presented here is
extendable to other contact problems in glaciology, such as that of subglacial
cavitation. The analysis of this problem and its discretisation is complicated
by the nonlinear rheology commonly used for modelling ice, the enforcement of a
friction boundary condition given by a power law, and the presence of rigid
modes in the velocity space, which render 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 specially-built projection operator onto the
subspace of rigid modes and a Korn-type inequality. These proofs rely on the
fact that the subspace of rigid modes is at most one-dimensional. Numerical
results are reported to validate the error estimates.
