- (W)ENO schemes can have very high order
- (W)ENO schemes can be complemented by high-order Runge-Kutta steps
- Non-linear criteria can help to decide if e.g. shocks should be sharpened further (PPM)
- Subcell resolution (position of discontinuity within cell)
At some point only a finer grid helps:
- More grid points
- Non-equidistant grid
- Adaptively refined grid