Modeling and simulation of real-life processes often require the introduction of multiphysics problems, where different physical models are coupled together in one monolithic formulation. Each of the involved phenomena might operate in a different temporal scale. That causes additional difficulties in deriving robust discretization schemes. In this project, we would like to reduce the complexity of systems resulting from such multiscale multiphysics problems. We intend to develop and implement efficient numerical schemes and obtain error estimation using space-time Petrov-Galerkin approach.