1.order vs. 2.order

March 22, 2006, 08:48

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?

March 22, 2006, 09:02

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

March 23, 2006, 23:28

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.

March 25, 2006, 11:46

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

March 28, 2006, 06:33

> 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.

March 22, 2006, 08:48	1.order vs. 2.order	#1
Christian Guest Posts: n/a	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?

March 22, 2006, 09:02	Re: 1.order vs. 2.order	#2
al Guest Posts: n/a	see the reference in "Spectral/hp Element Methods for Computational Fluid Dynamics" by George Em Karniadakis, Spencer J. Sherwin

March 23, 2006, 23:28	Re: 1.order vs. 2.order	#3
Harish Guest Posts: n/a	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.

March 25, 2006, 11:46	Re: 1.order vs. 2.order	#4
vasanth Guest Posts: n/a	error (l2) decreases by two times for 2 nd order scheme as compared to first order scheme on refining the grid

March 28, 2006, 06:33	Re: 1.order vs. 2.order	#5
Jean-François Guest Posts: n/a	> 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.