Question

In comparison between linear and quadartic element, explain when to use for both in 2D and 3D

Answer 1

Linear Element:- A linear element, also known as first order element, has nodes only at corners. Hence it needs only a linear equation to represent the behaviour of the element.

Linear elements are best to use when dealing with geometrically biased shapes like square, rectangle, etc as they will give high accuracy in results. Also in 3D, linear elements can be used for perfect shapes like a cube.

Linear elements require less computational efforts and time, hence should be used where less computational power is available.

Quadratic element:- A quadratic element or second order element has nodes at corners in addition to nodes in between them. Hence it needs a quadratic element to represent the behaviour of the element.

Quadratic elements should be use where you need to capture a curvature.

Complex curvatures need higher order elements but also lead to exceptionally high cost of computation and increase in computational time.

Quadratic elements show even higher accuracy for geometrically biased shapes as well as complex geometries including curvatures.

Element selection is all about factors available to us. Quadratic elements can be used in simple geometries but it will add to computational effort , which is not preferred. It is very important to consider all such factors before proceeding. Above mentioned points are valid for both 2D and 3D.