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Survey: DG and Discontinuous Finite Element

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Old   August 6, 2008, 08:26
Default Survey: DG and Discontinuous Finite Element
  #1
Sergio Rossi
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Hi,

I would like to know how many of you guys write DG codes for NS/RANS. Also, I see a lot of work has been done on DG, but it looks like nobody explored Discontinuous Finite Elements in general, where test and basis (shape) functions need not be the same. Is there any reason for this, apart from the difficulty of proving stability theorems?

Best Regards,

Sergio
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Old   August 9, 2008, 08:20
Default Re: Survey: DG and Discontinuous Finite Element
  #2
jack
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A lot of work has been done with DGFEM framework. test function and basis function's different choice lead to different finit element method,if test function is identical to basis function ,it is called galerkin method...
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Old   August 12, 2008, 06:01
Default Re: Survey: DG and Discontinuous Finite Element
  #3
Jed
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What you were looking for is called a Petrov-Galerkin method which is widely used.
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Old   August 13, 2008, 03:33
Default Re: Survey: DG and Discontinuous Finite Element
  #4
Sergio Rossi
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Hi, Jack,

have you got any references? Thanks,

Best regards,

deltaquattro
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Old   August 13, 2008, 03:37
Default Re: Survey: DG and Discontinuous Finite Element
  #5
Sergio Rossi
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Hi, Jed,

I know the definition of Petrov-Galerkin method, thanks I was looking for specific references on Petrov-Galerkin methods in the field of DGFEM. Since DG with some numerical fluxes is nonlinearly stable for convection-diffusion equations, the main thrust to the use of Petrov-Galerkin methods seems to be lacking. However, it is strange that nobody tried it, anyway. So I was looking for references, ideally comparing classical DGFEM approach and general DFEM approach.

Best regards,

Sergio
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Old   August 13, 2008, 06:37
Default Re: Survey: DG and Discontinuous Finite Element
  #6
Jed
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So it sounds like you are interested in a Discontinuous Petrov-Galerkin method. This is the first of several papers by the same authors. I don't know of any comparative studies.

@article{bottasso2002dpg, title={{The discontinuous Petrov--Galerkin method for elliptic problems}}, author={Bottasso, C.L. and Micheletti, S. and Sacco, R.}, journal={Computer Methods in Applied Mechanics and Engineering}, volume={191}, number={31}, pages={3391--3409}, year={2002}, publisher={Elsevier} }

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Old   August 15, 2008, 07:42
Default Re: Survey: DG and Discontinuous Finite Element
  #7
Sergio Rossi
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Thank you very much, Jed, thatīs what I was looking for.

Best,

deltaquattro
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