Inequality constraints for solving a PDE

Question

I want to solve an Allen - Cahn type PDE with an inequality constraint. More precisely, this equation reads d/dt(u) = f(u) + d^2/dx^2(u) (Please consider d/dt as total time derivative and d^2/dx^2 as partial second derivative of a function). Function f(u) is a nonlinear function. I want to impose the constraint 0<u<1 to the solution at each time step. Is there anyway to pass this condition to nonlinear solver of FEniCS?

Thanks in advance

Answer 1

I believe there are SNES VI solver in PETSc for doing this. These are accessible through low-level PESTcSNESSolver interface or high-level NonlinearVariationalSolver where you need to set its nonlinear_solver parameter to snes. Check contact-vi-snes demo.