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Differential equations on manifolds

 

Hello all,

I've been curious about (FEM-based) computational frameworks for solving PDEs on (connected, compact, curved) Riemannian manifolds with (Lipschitz) continuous boundaries. Does anyone have any experience with this?

If one were to approach such a problem with FEniCS, at what level should they begin to look into extending (FIAT? FFC?) to allow for operations such as element assembly using an atlas of charts?

Thanks,
Harish


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