A thermo-mechanically coupled test case for axi-symmetric ice sheet flow

This paper presents a set of approximate, but highly accurate, numerical solutions to the equations governing the flow of an axi-symmetric ice sheet with thermo-mechanical coupling within the ice sheet. The solution is obtained by using a finite-element method. The accuracy of the method is verified by means of a careful comparison of the results obtained with the finite-element method and those obtained using a thin ice approximation to reduce the problem to a set of ordinary differential equations. Two of the sources for the differences between the finite-element solution and the reduced solution, namely the discretisation error and the error introduced by the thin ice approximation are investigated. The magnitudes of both these differences are estimated by solving a sequence of problems on a range of computational grids. Excellent agreement between the two sets of results is achieved. Results from a simple direct computation by the finite-element method are also presented.