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Hello, I am trying to understand the FE Tabulation data obtained from e. g . PetscFEComputeTabulation. Using a 2D mesh with a single triangle, first order, with vertices (0,0), (0,1), (1,0) (see msh file attached), and a single quadrature point
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<div style="font-family: Arial, sans-serif; font-size: 14px;">Hello,</div><div style="font-family: Arial, sans-serif; font-size: 14px;"><br></div><div style="font-family: Arial, sans-serif; font-size: 14px;">I am trying to understand the FE Tabulation data obtained from e.g . PetscFEComputeTabulation. Using a 2D mesh with a single triangle, first order, with vertices (0,0), (0,1), (1,0) (see msh file attached), and a single quadrature point at (1/3, 1/3), one gets Nb = 6, Nc = 2, Nq = 1, and the arrays for the basis and first derivatives are of sizes [Nq x Nb x Nc] = 12 and[Nq x Nb x Nc x dim] = 24, respectively<br></div><div style="font-family: Arial, sans-serif; font-size: 14px;"><br></div><div style="font-family: Arial, sans-serif; font-size: 14px;">The values of these two arrays are:</div><div style="font-family: Arial, sans-serif; font-size: 14px;">basis (T->T[0])<br></div><div style="font-family: Arial, sans-serif; font-size: 14px;">[-1/3, 0, 0, -1/3, 2/3, 0, </div><div style="font-family: Arial, sans-serif; font-size: 14px;"> 0, 2/3, 2/3, 0, 0, 2/3]</div><div style="font-family: Arial, sans-serif; font-size: 14px;"><br></div><div style="font-family: Arial, sans-serif; font-size: 14px;">deriv (T->T[1])<br></div><div style="font-family: Arial, sans-serif; font-size: 14px;">[-1/2, -1/2, 0, 0, 0, 0, </div><div style="font-family: Arial, sans-serif; font-size: 14px;"> -1/2, -1/2, 1/2, 0, 0, 0, </div><div style="font-family: Arial, sans-serif; font-size: 14px;"> 0, 0, 1/2, 0, 0, 1/2,</div><div style="font-family: Arial, sans-serif; font-size: 14px;"> 0, 0, 0, 0, 0, 1/2] <br></div><div style="font-family: Arial, sans-serif; font-size: 14px;"><br></div><div style="font-family: Arial, sans-serif; font-size: 14px;">How does one get these values? I can't quite find a way to relate them to evaluating the basis functions of a P1 triangle in the given quadrature point.<br></div><div style="font-family: Arial, sans-serif; font-size: 14px;"><br></div><div style="font-family: Arial, sans-serif; font-size: 14px;">Thanks,</div><div style="font-family: Arial, sans-serif; font-size: 14px;">Noam<br></div><div style="font-family: Arial, sans-serif; font-size: 14px;"><br></div><div style="font-family: Arial, sans-serif; font-size: 14px;"><br></div>