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The MINI mixed finite element for the Stokes problem: An experimental investigation
Super-convergence of order 1.5 in pressure and velocity has been
experimentally investigated for the two-dimensional Stokes problem discretised
with the MINI mixed finite element. Even though the classic mixed finite
element theory for the MINI element guarantees linear convergence for the total
error, recent theoretical results indicate that super-convergence of order 1.5
in pressure and of the linear part of the computed velocity to the piecewise
linear nodal interpolation of the exact velocity is in fact possible with
structured, three-directional triangular meshes. The numerical experiments
presented here suggest a more general validity of super-convergence of order
1.5, possibly to automatically generated and unstructured triangulations. In
addition, the approximating properties of the complete computed velocity have
been compared with the approximating properties of the piecewise-linear part of
the computed velocity, finding that the former is generally closer to the exact
velocity, whereas the latter conserves mass better
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