Set up weak form

mathematics
1

Hi, I am a new Fenics user, I just confused with set up the weak form for one equation, I appreciate it if someone can help me with this.
So I already derived the equation by FDM, just not sure how to write the weak form in fenics. The equation:
u(z,t)^(n+1)-u^(n)-4adelta_tCpi^2*(u(z,t)^(n+1))^3sec^2(pi(u(z,t)^(n+1)-B)/(A-B))*(d/dz(u(z,t)^(n+1)))^2=0, where a,A,B,C are constant, u^(n) is u at time level n.

Many thanks

2

Please formulate your mathematics using latex-syntax, i.e.
u^{n+1}(z, t)-.....
I would suggest you have a look at the fenics tutorial, to get used to the finite element method and weak formulations.

An even more detailed introduction can for instance be found at: 1. Introduction — Finite element course 2021.0 documentation