A sequential-adaptive strategy in space-time with application to consolidation of porous media

Journal article, 2015

Issues related to space-time adaptivity for a class of nonlinear and time-dependent problems are discussed. The dG(k)-methods are adopted for the time integration, and the a posteriori error control is based on the appropriate dual problem in space-time. One key ingredient is to decouple the error generation in space and time with a hierarchical decomposition of the discrete space of dual solutions. The main idea put forward in the paper is to increase the computational efficiency of the adaptive scheme by avoiding recursive adaptations of the whole time-mesh; rather, the space-mesh and the time-step defining each finite space-time slab are defined in a truly sequential fashion. The proposed adaptive strategy is applied to the coupled consolidation problem in geomechanics involving large deformations. Its performance is investigated with the aid of a numerical example in 2D.