In a recent article in the Journal of Computational Physics, Ahlkrona et al. present a method (ISCAL - Ice Sheet Coupled Approximation Levels) implemented in Elmer/Ice that uses an error estimate to identify areas where the shallow ice approximation (SIA) can and cannot be deployed. According to this estimate, those regions, where the shallowness assumption prevails can be switched to a - compared to the full-Stokes solution - extremely cheap SIA (simply by replacing the matrix entries in the system matrix of the linearized and discretized full-Stokes problem. In their article the authors demonstrate a reduction of CPU time by ISCAL on an in size reduced real world case of up to 75% compared to a full-Stokes simulation run of the same problem.
Ahlkrona, J., P. Lötstedt, N. Kirchner, and T. Zwinger, 2016. Dynamically coupling the non-linear Stokes equations with the shallow ice approximation in glaciology: Description and first applications of the ISCAL method. J. Comp. Phys., 308, 1-19, doi:.