Manufactured solutions and the numerical verification of isothermal, nonlinear, three-dimensional Stokes ice-sheet models
1State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Sciences, Beijing 100190, China
2Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA
3Beijing Computational Science Research Center, Beijing 100084, China
4Department of Scientific Computing, Florida State University, Tallahassee, FL 32306, USA
5Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Abstract. The technique of manufactured solutions is used for verification of computational models in many fields. In this paper we construct manufactured solutions for models of three-dimensional, isothermal, nonlinear Stokes flow in glaciers and ice sheets. The solution construction procedure starts with kinematic boundary conditions and is mainly based on the solution of a first-order partial differential equation for the ice velocity that satisfies the incompressibility condition. The manufactured solutions depend on the geometry of the ice sheet and other model parameters. Initial conditions are taken from the periodic geometry of a standard problem of the ISMIP-HOM benchmark tests and altered through the manufactured solution procedure to generate an analytic solution for the time-dependent flow problem. We then use this manufactured solution to verify a parallel, high-order accurate, finite element Stokes ice-sheet model. Results from the computational model show excellent agreement with the manufactured analytic solutions.