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?
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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
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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
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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. |
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