We study dynamical Galerkin schemes for evolutionary partial differential equations (PDEs), where the projection operator changes over time. When selecting a subset of basis functions, is non-differentiable in time and an integral formulation has to be used. analyze projected with respect existence uniqueness solution prove that non-smooth operators introduce dissipation, result which crucial a...

Abstract We present an algorithm for hp -adaptive collocation-based mesh-free numerical analysis of partial differential equations. Our solution procedure follows a well-established iterative solve–estimate–mark–refine paradigm. The solve phase relies on the Radial Basis Function-generated Finite Differences (RBF-FD) using point clouds generated by advancing front node positioning that supports...

Recent years have seen growing interest in intelligent game-based learning environments that simultaneously provide intelligent tutoring systems’ adaptive pedagogical functionalities and promote learners’ engagement through the rich narratives and situated challenges of games. A key research question posed by game-based learning is how to deliver effective adaptive scaffolding to support tailor...