High-Order Spline Upwind for Space-Time Isogeometric Analysis

We propose an isogeometric space-time method for the heat equation, with smooth splines approximation in both space and time. A stabilizing term, based on a linear combination of high-order artificial diffusions, is added to the Galerkin formulation. This term is designed in order to make the linear system triangular with respect to time, extending the classical idea of upwiding. In order to keep optimal accuracy, the stabilization is weighted and fully activated locally, where sharp layers are detected, in a nonlinear way. We perform numerical tests that assess the stable and accurate behavior of the method.