# Attempting to index an object that is already indexed **URL:** \ **Category:** variational formulation\ **Created:** [December 20, 2019, 9:54am UTC](https://fenicsproject.discourse.group/t/attempting-to-index-an-object-that-is-already-indexed/2127 "2019-12-20T09:54:55Z")\ **Posts on this page:** 3\ **Page:** 1
**Author:** ![rektangle](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/rektangle/32/689_2.png) [@rektangle](https://fenicsproject.discourse.group/u/rektangle)\ **Post date:** [December 20, 2019, 9:54am UTC](https://fenicsproject.discourse.group/t/attempting-to-index-an-object-that-is-already-indexed/2127/1 "2019-12-20T09:54:55Z")
Hello! I am extremely new to FEniCS. I am trying to integrate the following system: ![image](https://global.discourse-cdn.com/free1/uploads/fenicsproject1/original/1X/a6d458e05837f21b80e228925b164fe9c34fa692.png) I am using approach that is proposed in FEniCS for temporal derivaties: discretize it and iterate over time. Then, for each time step construct corresponding variational problem and solve it sequentially for all time steps. As a machine I am using google colab dolfin version: 2019.1.0 > from fenics import \* > T = 5.0 # final time > num\_steps = 500 # number of time steps > dt = T / num\_steps # time step size > mesh = UnitIntervalMesh(10) # Define mesh for the coordinate interval > P1 = FiniteElement(‘P’, interval, 1) # Define function space for system of pressure and throughput > element = MixedElement([P1, P1]) > V = FunctionSpace(mesh, element) > v\_1, v\_2 = TestFunctions(V) # Define test functions > u = Function(V) # Define functions for pressure and throughput > u\_n = Function(V) > u\_1, u\_2 = split(u) # Split system functions to access components > u\_n1, u\_n2 = split(u\_n) > k = Constant(dt) # Define expressions used in variational forms > two = Constant(2) > F = ((u\_1 - u\_n1) / k) \* v\_1 \* dx + div(u\_2) \* v\_1 \* dx > + two \* u\_1 \* div(u\_1) \* v\_2 \* dx + u\_2 \* abs(u\_2) \* v\_2 \* dx # Define variational problem > vtkfile\_u\_1 = File(‘transient\_system/u\_1.pvd’) #Create VTK files for visualization output > vtkfile\_u\_2 = File(‘transient\_system/u\_2.pvd’) > progress = Progress(‘Time-stepping’) # Create progress bar > set\_log\_level(LogLevel.PROGRESS) > t = 0 # Time-stepping > for n in range(num\_steps): > t += dt # Update current time > solve(F == 0, u) # Solve variational problem for time step > \_u\_1, \_u\_2, \_u\_3 = u.split() # Save solution to file (VTK) > vtkfile\_u\_1 \<\< (\_u\_1, t) > vtkfile\_u\_2 \<\< (\_u\_2, t) > vtkfile\_u\_3 \<\< (\_u\_3, t) > u\_n.assign(u) # Update previous solution > progress.update(t / T) # Update progress bar > interactive() # Hold plot The error message is: ## Calling FFC just-in-time (JIT) compiler, this may take some time. Attempting to index with (Ellipsis, Index(8)), but object is already indexed: UFLException Traceback (most recent call last) in () 5 6 # Solve variational problem for time step ----\> 7 solve(F == 0, u) 8 # Save solution to file (VTK) 9 \_u\_1, \_u\_2, \_u\_3 = u.split() 26 frames /usr/lib/python3/dist-packages/ufl/log.py in error(self, \*message) 170 “Write error message and raise an exception.” 171 self.\_log.error(\*message) → 172 raise self.\_exception\_type(self.\_format\_raw(\*message)) 173 174 def begin(self, \*message): UFLException: Attempting to index with (Ellipsis, Index(8)), but object is already indexed: ---
**Author:** ![kamensky](https://avatars.discourse-cdn.com/v4/letter/k/e95f7d/32.png) [@kamensky](https://fenicsproject.discourse.group/u/kamensky)\ **Post date:** [December 20, 2019, 5:13pm UTC](https://fenicsproject.discourse.group/t/attempting-to-index-an-object-that-is-already-indexed/2127/2 "2019-12-20T17:13:11Z")
The problem here is that the divergence operator is not defined for a scalar argument. If you want \partial f/ \partial x, for some function f, you can get this in UFL with `f.dx(0)`, i.e., the partial derivative in the 0^\text{th} spatial direction. Alternatively, you could take the 0^\text{th} component of the gradient, i.e., `grad(f)[0]`. ---
**Author:** ![rektangle](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/rektangle/32/689_2.png) [@rektangle](https://fenicsproject.discourse.group/u/rektangle)\ **Post date:** [December 23, 2019, 12:26pm UTC](https://fenicsproject.discourse.group/t/attempting-to-index-an-object-that-is-already-indexed/2127/3 "2019-12-23T12:26:29Z")
Thank you very much! It did help!