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Stokes problem with analytical solution
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As a first example, consider a 2D stationary Stokes problem
with homogeneous Dirichlet conditions in the whole boundary:
Body forces b
are chosen so that the exact solution is
Several mixed elements can be used to compute the solution.
Some of them verify inf-sup condition
and some others don't
The following pictures show results obtained using a uniform mesh of 20x20 Q2Q1 elements
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| Velocity |
Streamlines |
Pressure |
If LBB condition is not satisfied, spurious oscillations
spoilt pressure approximation. Figures below show results
obtained with a mesh of 20x20 Q1P0 and P1P1 elements
Taking into account that the proposed problem has got analytical solution,
it is easy to analyze convergence of the different pairs of elements.
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