When you open your eyes in the morning, you usually see what you expect to see. Often it will be your bedroom, with things where you left them before you went to sleep. What if you opened your eyes and unexpectedly found yourself in a steaming tropical jungle? Why do we have expectations about what is about to happen to us? Why do we get surprised when something unexpected happens to us? More g...

In this paper we consider new upscaling and homogenization methods for the pressure equation that are less sensitive to the boundary condition assumptions than many other published methods. We start from the discretized pressure equation and rely on the construction of subproblems with signii-cantly fewer unknowns, describing the behaviour of the solution of the ne-grid problem in suitable subs...