Hi everyone
I want to use FEM method to study the following equation
u_t+u_{xxxxt}+u_x+u^2*u_x=f x \in (0,1]) , t\in(0,1]
the boundary condition
u_x(0,t)=u_x(1,t)=u_{xx}(0,t)=u_{xx}(1,t)=0
now I choose the initial condition
u(x,0)=x^3(x-1)^3.
and I select proper function "f"
f= -x^3*exp(-t)*(x - 1)^3 -6*x*exp(-t)*(5*x^3 - 10*x^2 + 6*x - 1) +
3*x^2*exp(-t)*(x^6*exp(-2*t)*(x - 1)^6 + 1)*(2*x - 1)*(x - 1)^2;
such that the test exact solution
u(x,t)=exp(-t)x^3(x-1)^3
where the time discretization used Euler-forward method.
I have write the code by fenics to obtain the L2-error and convergence rate
,while it is always wrong,can you help me ? Thanks a lot
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