Basis functions p=1 in 2D quadrilateral mesh

Hello,

I am new to NGSolve. Could you tell me what basis functions are used for the L2(mesh, order=1), H1(mesh, order=1, orderinner=0) and FacetFESpace(mesh, order=1) spaces? For example, for L2, are they 1,x,y,xy?
Is there anyone that can help me out?

Thank you so much!

Yunhui

Hi Yunhui,

the L2 space uses a tensor product of Legendre Polynomials in x and y direction for quads.

For H1 the basis functions in the lowest order case are (1-x)*(1-y),x*(1-y),x*y,(1-x)*y. You don't need to set the orderinner flag for order=1.

The FacetFESpace uses also Legendre Polynomials, but independently on each face.

Best,
Michael

Hi Michael,

Thank you so much for your reply. It helps a lot.

Best wishes!
Yunhui