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can any any one help me to understand this paragraph

First, the model domain G is discretized with a FE mesh consisting of nodes i and corresponding elements $E_ k$ . Then, a secondary FV mesh is constructed by connecting the midpoints and barycenters of the elements surrounding node i creating a box $B _i$ around node i (voir la figure jointe)

Ma question est: what's the difference between $B_i$ and $E_k$? and who is $i$?

enter image description here

Thank's for the help.

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1 Answer 1

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For a rectangular grid, the geometrical shapes of the two boxes is identical. They become different when you use non-rectangular grids. Furthermore, you can choose to use different element functions on the primal ($E_k$) and dual ($B_i$) grids. The index $i$ refers to the particular primal mesh node (a vertex of the grid). $B_i$ is centered around the $i$-th node.

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  • $\begingroup$ Sorry but i don't understand. In what $E_k$ and $B_i$ are differents? please. $\endgroup$
    – phi
    Commented Aug 25, 2014 at 21:40
  • $\begingroup$ and can you help me to understand the difference with an image, please $\endgroup$
    – phi
    Commented Aug 25, 2014 at 21:54

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