Our field of expertise in high order methods includes pure spectral methods, hp spectral element methods and high order DG methods (both nodal, and modal).
High order methods are the natural evolution of low order methods and they beat them in accuracy per degree of freedom, numerical dissipation and suitability for new hardware paradigm.
The simulation community has been using for decades traditional or low order methods. In fact, the numerical core of actual simulation tools relies in low order methods such as Finite Differences, Finite Volumes, and low order Finite Elements methods.