vector expression in Expression

Question

Hi, everybody. I am a newer to fenics. So anyone's answer is helpful to me.

I want to get the below Expression.

f = Expression("x[0]", "x[1]", "u"), where u = Expression("x[0]", "x[1]").

So how do I get the right expression f ?

Answer 1

If you want to use f as a source term in a mixed formulation, you should create three separate expressions and dot each of them with the test functions, i.e.

 v0,v1,v2 = TestFunctions(V)
 f0 = Expression("sin(x[0])")
 f1 = Expression("2.")
 f2 = Expression(("cos(x[0])","sin(x[0])"))
 L = f0*v0 + f1*v1 + dot(f2,v2)

provided that V is the function space.

Comments

Great, your idea is good.

Thank you very much for your help and your patience !!!

Thanks.

Answer 2

  u = Expression(("x[0]", "x[1]"))

should work in 2D, but also consider using

u = SpatialCoordinate(mesh)

Comments

Sorry, maybe I didn't express my idea correctly.

Actually, I want to create an Expression like the below one:

f = Expression(( 'sin(x[0])', '2.0', ('cos(x[0])', 'sin(x[0])' ) ))

So how should I do ? Thank you very much !!!

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You are still not expressing yourself clearly.

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Sorry.

I mean I want to create an Expression, which is vector-valued and its third component also is vector-valued.

Am I clearly now ?

Answer 3

If you want a tensor Expression, you can do

 f = Expression((("sin(x[0])","2."),("cos(x[0])","sin(x[0])")))

Comments

But I want that the first and second components of the Expression are scalar, but the third one is vector-valued

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why do you want that?

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Because in my function, the source term f is like the above Expression.

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So you have a MixedFunctionSpace?

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Yeah, a MixedFunctionSpace.
And one of the MixedFunctionSpace components is vector-valued.