ValueError Using Piola Transformation in Linear Elasticity Problem (2D Linear Elasticity Problem Coupled to Nonlinear Reaction-Diffusion Equation)

[francesco-ballarin]

@vozcoban

u = ufl.TrialFunction(V)

....

F = I + ufl.grad(u)
F_inv = ufl.inv(F) # F^-1

....

problem = LinearProblem(a, L, bcs=[])

The definition of F_inv is definitely introducing a nonlinearity. In such case, u must be a dolfinx.fem.Function, and not a ufl.TrialFunction, and the problem is not a LinearProblem anymore. To solve a nonlinear problem you can use dolfinx builtin NewtonSolver, or use SNES from PETSc.

Is the piola transform introducing some sort of non-linearity?

Yes

Is it fine to create two function spaces

Yes

Should this problem be solved as a linear or nonlinear problem in FEniCSx?

Nonlinear, at least as it is currently stated.