18. A quadrilateral element in the figure is mapped into the reference element.

(a) A point P has a coordinate (x, y) = (Vi, y) in the physical element and (s, t) = (-Vi, t) in the parent element. Find the y and t coordinates of the point using iso-parametric mapping.

(b) Calculate the Jacobian matrix at the center of the element.

(c) Is the mapping valid? Explain your answer.

3 (0,2)

2(1,1)

4 (0,0)

(-1,1) '

/

3(1,1)

i (1,0) l(-l-l) 2(1,-1)