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Towards nonuniform distributions of unisolvent weights for Whitney finite element spaces on simplices: the edge element case

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Academic year: 2021

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Figure 1: Simplified visualization of the interaction among decisive ingredients or steps for the success of the multivariate high-order polynomial approximation
Figure 2: The dots represent the set Z(T , Q 3 ) for a 2-simplex T in R 2 and two differente choices of Q 3 : on the left the uniform distribution {q i = i/4 with i ∈ {1, 2, 3}}, on the right a non uniform distribution
Figure 3: The elements of the set Σ 1 (T , Q 3 ) supported on two different edges of T : on the right the edge [x 0 , x 2 ], on the bottom the edge [x 1 , x 2 ]
Figure 4: The sets X 1 (F ;Q 3 ) for a 2-simplex F (on the left) and X 1 (T , Q 2 ) for a 3-simplex T (on the right) for a uniform distribution of points.
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