Hi:

i want to develop a FEM code for the two dimensional lid driven problem in a rectangular region , i use 4 nodes quadrilateral element.

FEM need a Galenkin projection, and one must to evalute the integral. it need to use the Gauss quadrature, but i do not have the value at the gauss point ,how should i do? can i use a conventional trapezodial rule?

regards.

why don't you have the values at the gauss points? your 4-node quadrilateral element is defined by a set of shape functions that should allow you to evaluate the function on any point in space, based on the function values at the four nodes. if you use the trapezoidal rule, or any other arbitrary rule, you will most likely create inconsistencies within your discretization method. use the shape functions.