2022/11/04 by Loli, Gabriele, Sangalli, Giancarlo, Tesini, Paolo · 1 citation
#FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2211.02692
We propose an innovative isogeometric space-time method for the heat equation, with smooth splines approximation in both space and time. To enhance the stability of the method we add a stabilizing term, based on a linear combination of high-order artificial diffusions. This term is designed in order to make the linear system lower block-triangular, that is, lower triangular with respect to time. In order to keep optimal accuracy, the stabilization terms are further weighted in terms of the residual. Through a series of numerical experiments, we validate the method's capability, showcasing its stability and accuracy.