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I'm programming the nonlinear Stokes problem (with a finite element method),

$$\operatorname{div}(\mu(u)\nabla u+pI)=f$$

where $\mu(u)$ is the Glen's power flow law (typical for glaciers). I want to test the model with simple and realistic data. Do you know where can I find simple tests and realistic examples (e.g. a mesh of a glacier and the physical constants)?

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Testing and model inter-comparison have been an important part of glacier models developments. One of the main numerical modelling suites used by the glaciology community is Elmer Ice, a full-Stokes, finite element, ice sheet/ice flow model. As part of the effort to test models the community around Elmer Ice developed ISMIP-HOM (Ice Sheet Model Intercomparison Project-Higher-Order ice-sheet Model). ISMIP-HOM consists of five diagnostic and one prognostic experiments, for both 2-D and 3-D geometries. For all the tests, the full-Stokes equations are solved. One of the experiments has an analytical solution obtained from perturbation analysis.

The details of each experiment, including input data can be found at the ISMIP-HOM project page maintained by Frank Pattyn at: http://homepages.ulb.ac.be/~fpattyn/ismip/

Some papers that I would recommend looking at to find out more details about the experiments are:

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