0
$\begingroup$

I'm having a problem using local coordinates basis in my finite elements code, depending how i label the vertices, my results goes completly wrong, results of integral doesn't match and functions are not $0$ or $1$ on their vertices. and the book don't tell the right way to do that. I searched over internet and found nothing.

Let $V_1=(x_1,y_1),V_2=(x_2,y_2)$ and $V_3=(x_3,y_3)$ being vertex of a triangle and $A$ it's area, then, the local coordinates are giving by this matrix product:

$\begin{bmatrix} L_{1} \\ L_{2} \\ L_{3} \end{bmatrix} = \frac{1}{2A}\begin{bmatrix} x_2y_3 - x_3y_2 & y_2 - y_3 & x_{3} - x_{2} \\ x_3y_1 - x_1y_3 & y_3 - y_1 & x_{1} - x_{3} \\ x_1y_2 - x_2y_1 & y_1 - y_2 & x_{2} - x_{1} \end{bmatrix} \begin{bmatrix} 1 \\ x \\ y \end{bmatrix}$

If i choose the vertex $V_1=(0,1),V_2=(1/2,0),V_3=(-1/2,0)$, the result is right, but if i change $V_2$ and $V_3$, it's came completly wrong, since my mesh is big i can't check every element to know the right way to label it. How should i proceed? There's any way for me to know the right way to label it? There's another base that i could use that won't lead me to this problem?

$\endgroup$
1
$\begingroup$

I found another basis in a book called "Finite Elements- A Gentle introduction" from David Henwood. If someone else struggle with this, just check this book.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.