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Spectral Elements (5)
Convergence properties:
• In the FEM, let h be the element size and k the degree of the
piecewise polynomial in each element, then the convergence of
the method, obtained for h → 0 , is:
k 1
u− uh
2 = Ch +
L ( Ω)
• In the SEM, let N be the degree of the piecewise polynomial in
each element, then the convergence of the method, obtained
now for N →∞, is:
u− u = Ce −α
N
L
2 ( Ω)
N
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Spectral Elements (6)
Generation of spectral mesh and implementation in FEM code
• A dual mesh composed of macro and micro elements is used:
• The macro elements are built first, then the micro mesh is
generated according to the chosen N:
e.g. in Cast3m
mesh generator:
micro = pxspect2
macro n tol;
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