  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.
