Spectral Elements have been applied to various applications in computational engineering, and
enable reductions of computational resources respect to more traditional techniques like finite
elements or finite differences. The main advantage is their high order approach, which equals the
accuracy of low order methods while showing computational efficiency and suitability to parallel
computation. This work illustrates how Spectral Elements can be used to solve various problems
usually encountered in geophysics, such as the scalar acoustic equation and linear and non-linear
elasticity.