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 is the variable that is equal to 1 everywhere and q is to be solved
for. I try and do a strong form and end up with:
\int_cell phi * q = \int_cell phi * grad a + \int_face phi*( {{a}} -
a_interior ) * normal
where {{a}} is the average of the values of a on the faces.
This though leads to the horribly broken solution of q that has positive and
negative values and jumps when it should be smooth. Is the answer to use a
limiter or filter at this point? I am new to discontinuous galerkin but I
haven't seen a filter or limiter being used in local discontinuous galerkin
before.
I'm not an expert on DG either, so don't know how to help. But let me ask you
where the the face integral comes from? You're not integrating by parts
anywhere, after all.
Best
W.
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Wolfgang Bangerth email: [email protected]
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