# Analog of perfectly matched layers for finite element methods

Is there an analog of perfectly matched layers for finite element methods? References or small examples are much appreciated.

A perfectly matched layer (PML) is generally introduced as a continuous concept without reference to the discretization method. A damping term is multiplied by the advection operator: $$\frac{\partial}{\partial x} \rightarrow \frac{\partial}{\partial x}\left(\frac{1}{1 + i\sigma/\omega}\right)$$ If $\sigma$ is positive, the imaginary component in the above equation drives the standard oscillatory solution of a wave equation to be exponentially decaying. A simple way of implementing this would just modify the discretized equation everywhere in space and then assign the value of $\sigma$ to be zero everywhere except near the boundaries.