Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: Strongly monotone quasi-Newtonian flows

In this article, we develop the a priori and a posteriori error analysis of hp-version interior penalty discontinuous Galerkin finite element methods for strongly monotone quasi-Newtonian fluid flows in a bounded Lipschitz domain Ω ⊂ ℝd, d = 2, 3. In the latter case, computable upper and lower bounds on the error are derived in terms of a natural energy norm, which are explicit in the local mesh size and local polynomial degree of the approximating finite element method. A series of numerical experiments illustrate the performance of the proposed a posteriori error indicators within an automatic hp-adaptive refinement algorithm.

Moving along the mental time line influences the processing of future related words

Abstract concepts like numbers or time are thought to be represented in the more concrete domain of space and the sensorimotor system. For example, thinking of past or future events has a physical manifestation in backward or forward body sway, respectively. In the present study, we investigated the reverse effect: can passive whole-body motion influence the processing of temporal information? Participants were asked to categorize verbal stimuli to the concepts future or past while they were displaced forward and backward (Experiment 1), or upward and downward (Experiment 2). The results showed that future related verbal stimuli were categorized faster during forward as compared to backward motion. This finding supports the view that temporal events are represented along a mental time line and that the sensorimotor system is linked to that representation. We showed that body motion is not just an epiphenomenon of temporal thoughts. Passive whole-body motion can influence higher-order temporal cognition.