Space-time finite elements and adaptive strategy for the coupled poroelasticity problem

A space-time finite element method for the pore-elasticity problem is outlined. By establishing the appropriate dual problem in space-time, it is possible to establish an exact a posteriori error representation formula based on residuals and the dual solution. In particular, we focus on the error generation in time. An adaptive strategy in the time-domain is proposed, and its performance is investigated with the aid of a numerical example in 2D. In particular, the excellent precision of the error estimate, in terms of the effectivity index being close to unity, is noted.