I am working on solving Stokes equations and is curious why there is very few special algorithms dealing with Stokes equation using finite difference method? (I checked at least five CFD book, none of them talks about solving Stokes equation at all).
Can I assume that all the algorithm solving Navier-Stokes equation (e.g., artifical compressibility method) works fine for Stokes problems too?
Thanks a lot.
Rui ---- p.s. it seems that there are a huge amount of Stokes algorithm for solving Stokes equation using finite element method. why is that?
Re: Stokes algorithm?
Stokes equations being linear, a complete mathematical theory based on weak solutions is available. Since finite element methods are based on the weak formulation, they can make use of this rich body of theory to establish stability and convergence proofs. A priori and a posteriori error estimates can also be calculated which will be useful for adaptation. Hence a very complete theory can be built up for FEM which is not possible with other schemes.
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