The Cryosphere Manufactured solutions and the verification of three-dimensional

Abstract. The manufactured solution technique is used for the verification of computational models in many fields. In this paper, we construct manufactured solutions for the three-dimensional, isothermal, nonlinear Stokes model for flows in glaciers and ice sheets. The solution construction proce-dure starts with kinematic boundary conditions and is mainly based on the solution of a first-order partial differential equa-tion for the ice velocity that satisfies the incompressibility condition. The manufactured solutions depend on the geom-etry of the ice sheet, basal sliding parameters, and ice soft-ness. Initial conditions are taken from the periodic geometry of a standard problem of the ISMIP-HOM benchmark tests. The upper surface is altered through the manufactured solu-tion procedure to generate an analytic solution for the time-dependent flow problem. We then use this manufactured so-lution to verify a parallel, high-order accurate, finite element Stokes ice-sheet model. Simulation results from the compu-tational model show good convergence to the manufactured analytic solution.