Problem 1

The variational formulation that you need to specify in the file Bistable.m is given by

    u*v*dx + k*0.01*du'*dv*dx

for the left-hand side and

    k*w(2)*(1 - w(2)*w(2))*v*dx + w(1)*v*dx

for the right-hand side.

The fixed-point iteration can be implemented as follows:

  while 1

    % Assemble vector
    b = AssembleVector(p, e, t, 'Bistable', [U0 U1], time);
    
    % Solve the linear system
    newU1 = A \ b;
    
    % Check if the solution has converged
    if norm(newU1 - U1) < 0.01
      break;
    end
    
    % Update U1 to new value
    U1 = newU1;

  end