UFL L^1-Norm of a function

Question

Is there any natural way to define with UFL the L ^ 1-Norm of a function's coefficients as a Functional? || u ||1 = sum(abs(u.vector()))

Can you place non-negative restrictions on the domain of this Functional?

Any help is appreciated!

Comments

Hi Andre,

Could you please improve the formatting of your question?

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Hi Marie, yes I could. I am looking for alternatives to using FEniCS project in
optimization problems. I need to minimize the L^1 norm (functional).

I know that L^2 norm can be defined as

    u = Function(V)
    F = Functional(inner(u, u)*dx)

But what about L^1 norm?

    ||u||1 = sum(abs(u.vector()))

Is there a natural way of defining this type of norm trough the ufl?

Answer 1

# The quadrature is not exact as integrand (in mathematical sense)
# is not polynomial - UFL, in fact, operates DOF-wise and keeps
# polynomial basis.
F = abs(u)*dx

# Customize quadrature
F = abs(u)*dx(None, {'quadrature_degre': 5})

Comments

Jan,
thanks for the help.