Before revision:   Next, we introduce a  space-time (tensorproduct) discretization using finite elements in space and piecewise linear functions in time .
After revision:  We propose to utilize a well-posed inf-sup stable framework of the PDE in appropriate Lebesgue-Bochner spaces. Next, we introduce a space-time (tensorproduct) discretization using finite elements in space and piecewise linear functions in time .