slope limiter of discontinuous Galerkin on triangular element(2D, P2 polynomial)

effort8 · January 17, 2012, 03:02

Hello, friends!!
These days I'm studying discontinuous Galerkin method.
And I'm computing 2D Burgers equation for test problem.

I have to use slope limiter due to spurious oscillations.
The slope limiter of P1 polynomial was explained well in Cockburn & Shu paper.
(The Runge-Kutta discontinuous Galerkin method for conservation laws V)

For the P2 case, the solutions are defined at the three mid-point of edges and the three vertices on triangular element.
TVB limiter is just considered at the three mid-point of edges.
Thus, we can compute the limited solution at the three mid-point of edges (It is easy.).
But we have to consider the solutoin at the three vertices for the P2 case.

How to obtain limited solution at the three vertices on triangular element?

I would appreciate it if anyone give me some comments.

Thanks!!

zqb0929 · March 19, 2012, 09:03

i think the slope limiter should be applied to limit the the linear part of the numerical solutions(no matter how high order polynomials) and higher parts remain unchanged. we should limit the three values of mid-point of three sides which are computed from the linear part of the numerical solutions.maybe i am wrong.

January 17, 2012, 03:02	slope limiter of DG method	#1
effort8 New Member DJChoi Join Date: Jan 2012 Posts: 8 Rep Power: 14	Hello, friends!! These days I'm studying discontinuous Galerkin method. And I'm computing 2D Burgers equation for test problem. I have to use slope limiter due to spurious oscillations. The slope limiter of P1 polynomial was explained well in Cockburn & Shu paper. (The Runge-Kutta discontinuous Galerkin method for conservation laws V) For the P2 case, the solutions are defined at the three mid-point of edges and the three vertices on triangular element. TVB limiter is just considered at the three mid-point of edges. Thus, we can compute the limited solution at the three mid-point of edges (It is easy.). But we have to consider the solutoin at the three vertices for the P2 case. How to obtain limited solution at the three vertices on triangular element? I would appreciate it if anyone give me some comments. Thanks!! Last edited by effort8; January 27, 2012 at 05:16.

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March 19, 2012, 09:03		#2
zqb0929 New Member Join Date: Sep 2011 Posts: 11 Rep Power: 14	i think the slope limiter should be applied to limit the the linear part of the numerical solutions(no matter how high order polynomials) and higher parts remain unchanged. we should limit the three values of mid-point of three sides which are computed from the linear part of the numerical solutions.maybe i am wrong.