Thanks for the response Praveen,
What I am getting is he image that was in the initial post but here it is
again for convenience.
The correct value is in black and is perfectly 0. The calculated values are
in white and are on the order of 10^(-12).
The advection equation is solved with a conju
The scheme you wrote looks fine. If a=1, then you should get q=0 or something
close to machine zero. What are you getting ? Here you are projecting the
gradient onto a discontinuous polynomial space. The blowup probably happens
when you solve your advection equation, and maybe you need to look t
Thanks again for your time I really do appreciate it and don't want to
waste it. The added equation, although it is an advection equaiont, it is
actually representing a diffusion term in the hyperbolic equation. Its just
an intermediate term needed for local discontinuous galerkin. Using
averag
On 7/19/24 14:37, Sean Johnson wrote:
Would an equation so simple need stabilizing?
Yes. It's an advection equation with no diffusion. There needs to be some kind
of stabilization. At the very least you will have to use an upwind flux somewhere.
Best
W>
--
I am following the process from "Nodal Discontinuous Galerkin Methods" by
Jan S. Hesthaven and Tim Warburton. It might be particular to discontinuous
galerkin to do it this way but I claim to be no expert.
Regardless, if I do the same integral in weak form it still results the
same. The equatio
On 7/19/24 14:10, Sean Johnson wrote:
I integrating by parts on the phi * grad a. First time gets it into weak form.
Then a second time gets it back into the original equation and into strong
form as I understand it. Is this misunderstood?
That's at least unusual, to integrate twice. I've ne
I integrating by parts on the phi * grad a. First time gets it into weak
form. Then a second time gets it back into the original equation and into
strong form as I understand it. Is this misunderstood?
On Friday, July 19, 2024 at 2:01:32 PM UTC-6 Wolfgang Bangerth wrote:
> On 7/19/24 13:35, Sea
On 7/19/24 13:35, Sean Johnson wrote:
The term shown in the graph is from a fairly simple equation. It arises from
the need of using the Local Discontinuous Galerkin method for a second order
derivative in one of the hyperbolic equations. The equation being solved is:
grad a - q = 0
where a i
Thanks for the response. I am totally open to the idea of the algorithm not
being stable.
The term shown in the graph is from a fairly simple equation. It arises
from the need of using the Local Discontinuous Galerkin method for a second
order derivative in one of the hyperbolic equations. The
Sean:
VectorTools::interpolate(mapping,dof_handler_DG,Functions::ConstantFunction(1.),alpha_solution);
Obviously changing the final vector for different variables.
Later, when the gradient of these terms are used the gradient calculated by
deal.ii is not 0. I do get very small values on the
Hey,
I am trying to solve a few coupled hyperbolic equations using discontinuous
galerkin finite elements.
In one of my test cases there are oscillations forming. I tracked it down
to the gradients of variables that are set to 1 everywhere by:
VectorTools::interpolate(mapping,dof_handler_DG,Fu
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