# Local Coordinates and Global Coordinates in Finite Element Analysis

Monday, January 20, 2014 18:08## Local Coordinates

A local coordinates system whose origin is located within the element in order to simplify the algebraic manipulations in the derivation of the element matrix.

- The use of natural coordinates in expressing approximate functions is advantageous because special integration formulas can often be applied to evaluate the integrals in the element matrix.
- Natural coordinates also play a crucial role in the development of elements with carved boundaries.

### Natural Coordinates

It is a local coordinate system that permits the specification of a point within the element by a dimensionless parameter whose absolute magnitude never exceeds unity.

- It is dimension less.
- They are defined with respect to the element rather than with reference to the global coordinates.

## Global Coordinates

Global coordinates are convenient for specifying the location of each node, the orientation of each element, the boundary conditions and the loads for the entire domain.

- The solution to the field variable is generally represented with respect to the global coordinates.

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