# Equivalent to Expression for a vector valued function in dolfinx?

**URL:** <https://fenicsproject.discourse.group/t/equivalent-to-expression-for-a-vector-valued-function-in-dolfinx/8669>\
**Category:** Uncategorized\
**Created:** [July 1, 2022, 3:11pm UTC](https://fenicsproject.discourse.group/t/equivalent-to-expression-for-a-vector-valued-function-in-dolfinx/8669 "2022-07-01T15:11:11Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![Foteini\_Karakatsani](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/foteini_karakatsani/32/3876_2.png) [@Foteini\_Karakatsani](https://fenicsproject.discourse.group/u/Foteini_Karakatsani)\
**Post date:** [July 1, 2022, 3:11pm UTC](https://fenicsproject.discourse.group/t/equivalent-to-expression-for-a-vector-valued-function-in-dolfinx/8669/1 "2022-07-01T15:11:11Z")

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Hello,

I would like to define the exact solution for a time dependent stokes problem. I used to use Expression in fenics to do this. How can I define a vector valued function in fenicsx?

I have written the following code but it does not work

class exact\_solution1():  
def **init** (self):  
self.t = 0.0  
def eval(self, x):  
print(x.shape[1])  
t = self.t  
return np.full(x.shape[1], (pow(t,2)_(pow(x[0],4)-2_pow(x[0],3)+ pow(x[0],2))_(4_pow(x[1],3)-6_pow(x[1],2)+ 2_x[1]), -pow(t,2)_(pow(x[1],4)-2_pow(x[1],3)+ pow(x[1],2))_(4_pow(x[0],3)-6_pow(x[0],2)+ 2_x[0])))

I would be grateful if someone can help me with this!

Thank you in advance!  
Fotini

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**Author:** ![nate](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/nate/32/17_2.png) [@nate](https://fenicsproject.discourse.group/u/nate)\
**Post date:** [July 1, 2022, 3:16pm UTC](https://fenicsproject.discourse.group/t/equivalent-to-expression-for-a-vector-valued-function-in-dolfinx/8669/2 "2022-07-01T15:16:25Z")

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See e.g: [This vector function definition](https://bitbucket.org/nate-sime/dolfin_dg/src/af91d0a33eb1de5e97ddaeaaeefc477403e124f0/demo/dolfinx/stokes/dg_stokes_block.py#lines-22:26) which is [interpolated into an appropriate space](https://bitbucket.org/nate-sime/dolfin_dg/src/af91d0a33eb1de5e97ddaeaaeefc477403e124f0/demo/dolfinx/stokes/dg_stokes_block.py#lines-54:55) for [error computation](https://bitbucket.org/nate-sime/dolfin_dg/src/af91d0a33eb1de5e97ddaeaaeefc477403e124f0/demo/dolfinx/stokes/dg_stokes_block.py#lines-210:213).

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**Author:** ![Foteini\_Karakatsani](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/foteini_karakatsani/32/3876_2.png) [@Foteini\_Karakatsani](https://fenicsproject.discourse.group/u/Foteini_Karakatsani)\
**Post date:** [July 1, 2022, 6:31pm UTC](https://fenicsproject.discourse.group/t/equivalent-to-expression-for-a-vector-valued-function-in-dolfinx/8669/3 "2022-07-01T18:31:44Z")

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Thank you so much! Very helpful!