The author is interested in an initial-boundary value problem for the Sobolev equation, written in the form \[ cu_t+d\cdot\nabla u-\nabla\cdot(a\nabla u+b\nabla u_t)=f, \] where \(u_t\) denotes \(\partial u/\partial t\). The equation is defined on a region \(\Omega\times I\), with a bounded domain \(\Omega\) in three or fewer dimensions and a finite interval in time \(I=[0,T]\). The initial conditions are of the form \(u(x,0)=u_0\), and Dirichlet boundary conditions hold in space, \(u(x,t)=0\) for \(x\in\partial\Omega\). The equation is discretized by first dividing the time interval \(I\) into subintervals \(I_n\), and then for each \(n\) dividing \(\Omega\) into sets of elements \({\mathcal T}_n\). The maximum diameter of elements in \({\mathcal T}_n\) for all \(n\) is denoted \(h\). Trial functions are then taken in the form \(p(x)q(t)\) where \(p(x)\) is a continuous piecewise polynomial of degree \(r\) and \(q(t)\) is a polynomial of the same degree \(r\). The spatial subdivision of \({\mathcal T}_n\) is chosen independent of the subdivision for different values of \(n\), and temporal continuity is not assumed between \(I_N\) and \(I_{n+1}\). The author goes on to formulate a streamline diffusion finite element method (F.E.M.), with the streamline diffusion term of the form \(\delta(cv_t+d\cdot\nabla v-\nabla(b\nabla v_t))\) and with the temporal discontinuity entering as a jump term. The parameter \(\delta\) is chosen proportional to \(h\) for larger \(h\) and proportional to \(h^2\) for smaller \(h\). He proves three theorems. The author first proves a coercivity lemma and then a stability theorem, bounding the approximate solution in terms of \(f\) and \(u_0\) for both choices of \(\delta\). Finally, assuming a smooth solution of the continuous problem, he proves two error estimates corresponding to the two choices of \(\delta\).