novel model order reduction framework for space and time domain discretizations is proposed. Iterative convergence of a Galerkin approximation in space and a Least Squares Petrov Galerkin approximation in time is obtained through a staggered reduced basis method in space-time. In every iteration, one of the two domains (space or time) is refined; and the other is reduced and a posteriori error indicators in space and time are used to drive the convergence iterations. Numerical results for 2D heat transfer and convection-diffusion problems demonstrate the significant computational efficiency of the proposed methodology. Comparisons of wall-clock times and solution accuracy with traditional time integration algorithms has been presented to validate the efficacy of the proposed framework and demonstrate computational savings of an order of magnitude. (C) 2017 Elsevier Ltd. All rights reserved.