Discontinuous Galerkin / jump operators

Question

Hello,
Is the following jump operator implemented in fenics

$$[ u ] = u^+ \otimes n^+ + u^- \otimes n^-$$

where u is a vector and

$$u \otimes n = (u_i n_j)_{(ij)}$$

Thank you

Comments

Shouldn't there be plus or minus sign between outer products in the first equation?

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hoops ... very sorry for the mistakes.

[ u ] = u^+ \otimes n^+ + u^- \otimes u^-

u \otimes n = (u_i n_j)_{(ij)}

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Ok, answer given. Please, edit question appropriately.

Answer 1

def tensor_jump(u, n):
    return outer(u('+'), n('+')) + outer(u('-'), n('-'))

Comments

Thank you very much !

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jump(outer(u, n))

represents rather $u^+ \otimes n^+ - u^- \otimes n^-$ according to ufl/ufl/operators.py. Correct answer is

def tensor_jump(u, n):
    return outer(u('+'), n('+')) + outer(u('-'), n('-'))

Answer edited. One can mask it into jump(v, n) function using compound outer operator

def tensor_jump(u, n):
    return jump(outer(u, n, n), n)

but that's rather obfuscation than simplification.

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Or

def tensor_jump(u, n):
    dim = n.shape()[0]
    I = Identity(dim)
    return jump(outer(u, I), n)

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It is clear with the definition given in ufl/ufl/operators.py.
Thank you very much for your help.