Experienced in Numerical methods used to solve finite volume and finite elements method problems.
As a work sample , I have made a code to simulate a metal hydride absorption/desorption problem using finite volume method , 2nd order full implicit transient scheme and Tri diagonal matrix method to solve the linear equations.
these types of problems comes under the category of diffusion.
In your problem description , All the 3 schemes can be used , the variable boundary conditions can be applied (3 insulation (zero heat flux) and 1 source ) . The 3 different time step size would be used for transient till t=1 and steady state equation can also be solved ( by eliminating the transient term) .
Please see I don't have any experience in GMRES algorithm as we only use Multigrid method or TDMA method for solving the equation. it could take me a while.
some query
1. ) in error formula , U analytical has to be provided by the client
2.) convergence criteria not defined