I noticed that when I use linear shape functions with an increasing mesh x
resolution, the solution seems to approach euler-bernoulli ode solution.
however, when I use higher order shape functions, fem solution do not converge
as the linear shape function case.
This would be concerning. The finite element approximation should converge to
the same solution whether you use linear or quadratic elements. It should just
converge faster with quadratic elements, but the limit point of the
convergence needs to be the same.
If that's not the case, it's worth exploring why that would be so, perhaps
starting with articulating how exactly the two limits differ.
Best
W.
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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