[mb.pejvak]

I started learning FEM and I just started reading a literature about Discontinuous Galerkin, which as I understood is combination of FEM and FVM. But what came to my mind is that what is the advantages of Discontinuous Galerkin over using FVM, since Discontinuous Galerkin seems more complicated.

[vesp]

a) locally spectral approximation with arbitrary order of accuracy
b) compact communication stencil, trivial to parallelize
c) probably more

[Ford Prefect]

Originally Posted by vesp

a) locally spectral approximation with arbitrary order of accuracy
b) compact communication stencil, trivial to parallelize
c) probably more

Could you please elaborate a bit on b) with regards to FVM?

[vesp]

Originally Posted by Ford Prefect

Could you please elaborate a bit on b) with regards to FVM?

regardless of the order, communication is always only between direct neighbors. in high order fv, the stencils grows, thus requiring more communication partners.

[mb.pejvak]

Originally Posted by vesp

a) locally spectral approximation with arbitrary order of accuracy
b) compact communication stencil, trivial to parallelize
c) probably more

Thanks for your comments. But despite the advantages of dG, why is fvm still dominated approach in CFD

[el_mojito]

Originally Posted by mb.pejvak

Thanks for your comments. But despite the advantages of dG, why is fvm still dominated approach in CFD

For one it's more complex in every regard. Starting at the principal mathematical analysis of the method to coding a DG solver right up to visualizing the results from a simulation.

[FMDenaro]

Originally Posted by mb.pejvak

Thanks for your comments. But despite the advantages of dG, why is fvm still dominated approach in CFD

FVM is actually a special case of the FEM forumulation. It is largely used because the resulting weak form correspond to a physical conservation law according to the fundation given by the Reynolds transport theorem.

[mb.pejvak]

Originally Posted by FMDenaro

FVM is actually a special case of the FEM formulation. It is largely used because the resulting weak form correspond to a physical conservation law according to the foundation given by the Reynolds transport theorem.

Yeah FVM can be achieved by FD and FE methods, but dG has some advantages over both, in particular FVM, some of which mentioned by @vesp.

Originally Posted by el_mojito

For one it's more complex in every regard. Starting at the principal mathematical analysis of the method to coding a DG solver right up to visualizing the results from a simulation.

Definitely accuracy has computational cost, nothing is free except HIV . But my question is in which condition worth paying the price. or in another word, how much cost should be paid for the accuracy (I know my question is over-general, but I want to some example which make better sense). Any reference to book or paper would be appreciated.

[mb.pejvak]

This discussion can be to some extend helpful regarding the question
https://www.researchgate.net/post/Li...method_for_CFD