1.order vs. 2.order
 

It is (to my belief) generally known and accepted that 2.order discretization is preferred to 1.order discretization. But I cannot recall reading any books or articles testing this. Can anyone please help me with references?

Re: 1.order vs. 2.order
 

see the reference in "Spectral/hp Element Methods for Computational Fluid Dynamics" by George Em Karniadakis, Spencer J. Sherwin

Re: 1.order vs. 2.order
 

First order discretization is usually dissipative and 2 order tend to be more dispersive.

Computational fluid mechanics and heat transfer - pletcher et .. is a good read on this topic in the context of FDM.

Re: 1.order vs. 2.order
 

error (l2) decreases by two times for 2 nd order scheme as compared to first order scheme on refining the grid

Re: 1.order vs. 2.order
 

> error (l2) decreases by two times for 2 nd order scheme as compared to first order scheme on refining the grid

Furthermore, what are called first order schemes are generally schemes based on a constant reconstruction which are not consistent on non-uniform meshes.