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I wanted to learn how to implement a code for the Stokes and Navier--Stokes equations 2D/3D. I already know how to implement it when the elements are triangles or tetrahedral.

Do exists finite element schemes using only square/cube elements for the pressure and velocity? Can you suggest me some paper or book with the method?

Thanks in advance.

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    $\begingroup$ If you know how to implement tria/tetra elements, then it is straightforward to implement quad/hex elements. You need to modifications to account for the change in the number of nodes and implement appropriate subroutines for the basis functions and quadrature points.. You can refer to my repository for the details. $\endgroup$ – Chenna K Jul 19 at 22:01
  • $\begingroup$ Thanks @Chenna K. But, for example, in the case of a mesh composed by triangles T, we build the set of base functions P1(T) (set of polynomial of degree less that one on a triangle T of the mesh) such that the value of one element in one node is 1 and 0 in the other nodes, how can build the basis functions in squares (for example)? I think that it is the only big difference. A more specific question: in a reference triangle T, the base is {1-x-y,x,y}, but which is the base on a reference square? $\endgroup$ – yemino Jul 19 at 22:41
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    $\begingroup$ Basis functions for quad/hex elements are formed by taking the tensor product of basis functions in 1D. Refer to this page for the details. $\endgroup$ – Chenna K Jul 20 at 0:10

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