# In the generation of element geometries, if dx dy represents an area element in the real element and dεdη represents the corresponding area element in the master element, then what is the expression for Jacobian j^e?

In the generation of element geometries, if dx dy represents an area element in the real element and dεdη represents the corresponding area element in the master element, then what is the expression for Jacobian j^e?

(a) (dx dy) (dεdη)

(b) $\frac{dx}{d\epsilon} \frac{dy}{d\eta}$

(c) $\frac{d\epsilon}{dx} \frac{d\eta}{dy}$

(d) $\frac{1}{(dx dy) (d\epsilon d\eta)}$

This interesting question is from Modelling Considerations topic in division Interpolation Functions, Numerical Integration and Modelling Considerations of Finite Element Method

by (185k points)
selected by

The correct option is (b) $\frac{dx}{d\epsilon} \frac{dy}{d\eta}$

Explanation: The numerical evaluation of integrals over actual elements involves a one-to-one mapping between the actual element and the master element. This requirement can be expressed as j^e>0, where j^e is the Jacobian matrix. J^e represents the ratio of an area element in the real element to the corresponding area element in the master element.

+1 vote
+1 vote
+1 vote
+1 vote
+1 vote
+1 vote
+1 vote
+1 vote
+1 vote
+1 vote
+1 vote
+1 vote
+1 vote