Hello, teacher, Can freefem++ write 1D discontinuous Galerkin FEM code?
yes you can !
except periodic boundary condition (no jump, mean, on periodic boundary ).
Hello, in fact, if there is a jump on periodic boundary, can freefem++ not implement the 1D discontinuous Galerkin FEM code?
Yes the jump and mean function is implémentée in version 4.11,
I have try it ok for my se thé exemple
Hello, as shown in the figure, this is a 1D discontinuous finite element problem. If I want to realize the above boundary term (the second term in the last line)in FreeFem++, how can I achieve it? thank you
Read thé CHANGELOG.md file for the syntaxe, sorry the doc is not updated:
- DG formulation in 1d : add integral of all border of element :
intallBE(ThL)and unified the notation by addingintallBE(ThS),intallBE(Th2),intallBE(Th3)nuVertexof now the vertex number of element in intallBE0d integralBoundaryBE,InternalBEto know if border element (BE) is on true boundary of not. updatenElementonBin case on no manifold data (value greater > 2) in meshL, MeshS case … add code to use jump, mean of test functuon on MeshL case. ( not in mesh3 ) to compute RHS.
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Hello, thank you for your reply. I understand, but How will this symbol be implemented?
u+ refers to the value on the right of the oriented edge
Hello, in freefem++, about the one-dimensional discontinuous finite element method, on two adjacent intervals, on the common endpoint K of elements e1 and e2, how to represent the value of this point when k is on the first element?
I am not sure thaï u_xx is defined , I will se to morrow!
the the way the get the otherside de value is
otherside(u)
If I make no mistake you formula is
intallBE(Th)((dxx(u)*jump(v)-dyy(v)jump(u))(N.x>0)/lenEdge)
Hello, thank you for your answer. The value u^ (+) of the right cell and the value u^ (-) of the left cell are taken on the adjacent cell. How to distinguish these two values when programming? That is, how to define the boundary item u^ (+) *v^ (-) or u^ (-) *v^ (+)?
intallBE(Th)(u^(+)*v^(-))?
intallBE(Th)(u^(-)*v^(+))?
intallBE mean you are on left or right on the segment so all point are vue 2 times.
It is why, I had (N.x > 0) to get just take the right value
it is impossible of write intallBE(Th)(u^(+)*v^(-))because it is non local
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Hello, I have a boundary item, i.e. U0 ^ {+} * U1 ^ {-} on \ partial \ Omega. Use this command intallbe (th) (U0 * (N.x> 0) * otherside (U1) * jump (V)/lenEdge). Is it correct?
I think no if it is a true boundary because otherside have no sens and ìntallbe do the integration on all triangle boundary.
Hello, in fact, this is my boundary condition,
where f is the flux, p = 2.,
Expand the flux by u ^ {+} * u ^ {+} + u ^ {+} * u ^ {-} + u ^ {-} * u ^ {-}, then the above boundary condition is
Σ (jump (v) * (u ^ {+} * u ^ {+} + u ^ {+} * u ^ {-} + u ^ {-} * u ^ {-}), this command
intallBE (Th) (jump (v) * (u* u * (N.x > 0) + u* u + u * u * (N.x < 0)) / lenEdge), is it correct?
remark, you schema is def at point and in freefem you have finite element function
so if you take P1dcL1 finite element when the dof is the value a vertex
so u_m^- == u[2m] and u_m^+ == u[][2m+1]
where m is ne element element
load "msh3"
load "Element_P1dc1"
meshL Th=segment(10);
fespace Vh(Th,P1dcL1);
Vh u=x;
cout << u[] << endl; // to see
for(int m=0;m<10;++m)
{
cout << " u_m^- " << u[][2*m] << " ";
cout << " u_m^+ " << u[][2*m+1] << endl;
}
Hello, thank you for your reply, in fact, I developed the numerical flux of boundary conditions f = u ^ {+} * u ^ {+} + u ^ {+} * u ^ {-} + u ^ {-} *u ^ {-},p=1, this how to say in FreeFem++?
I want to know if I have the right boundary conditions?
intallBE(th)(jump(v)(uu*(N.x>0)+uu+uu*(N.x<0)))
Hello, according to your answer, if u_m ^ - is N.x < 0, then intallBE (th) (u (N.x> 0) * u * (N.x < 0) * jump (v))* on the boundary is a nonlinear term?
Hi, Frédéric,
if i understand it correctly, at this moment, DG in a periodic domain is not supported within freefem, right? thank you very much.
yes, the jump, mean are not correct with periodic BC.
understood, i guess it will be potentially fixed in newer version of freefem, right?