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In Jasak's Ph.D. thesis (2000), a notion is given about discretization of a transport equation: For good accuracy, it is necessary for the order of the discretization to be equal to or higher than the order of the equation that is being discretized.
Question:
Why?

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    $\begingroup$ How do you define good accuracy? How much accuracy is good? It's a pretty bad idea to use good or bad for something that could be measured quantitatively. $\endgroup$ – Alone Programmer Apr 20 '20 at 16:24
  • $\begingroup$ Putting away the definition of good accuracy, does PDE order dictate any requirement or optimum choice for discretization order? $\endgroup$ – Alish Apr 20 '20 at 18:33
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    $\begingroup$ No. I see no connection between the two. $\endgroup$ – Wolfgang Bangerth Apr 20 '20 at 20:39
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    $\begingroup$ If you were doing FEM, say for the Poisson problem, you wouldn't want to use DG0 space discretization because the corresponding bilinear form $-\left<\{Q\nabla u\cdot\hat{n}\},[v]\right> + \sigma \left<[u],\{Q\nabla v\cdot\hat{n}\}\right> + \kappa \left<\{h^{-1}Q\}[u],[v]\right>$ would be all zeros except for the contribution from the penalty term $\kappa \left<\{h^{-1}Q\}[u],[v]\right>$. Still there is nothing wrong with it as far as I know, just doesn't feel good. $\endgroup$ – Abdullah Ali Sivas Apr 21 '20 at 14:58
  • $\begingroup$ @AbdullahAliSivas, How if I do FVM? Can a similar argument be applied there? $\endgroup$ – Alish Apr 22 '20 at 20:06

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