In this paper, we consider a 2nd order semilinear parabolic initial boundary value problem (IBVP) on a bounded domain $\Omega \subset {ℝ}^N$, with nonstandard boundary conditions (BCs). More precisely, at some part of the boundary we impose a Neumann BC containing an unknown additive space-constant $\alpha \left(t\right)$, accompanied with a nonlocal (integral) Dirichlet side condition. We design a numerical scheme for the approximation of a weak solution to the IBVP and derive error estimates for the approximation of the solution $u$ and...