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.

翻译：我们针对热方程提出了一种创新的等几何时空方法，该方法在空间和时间上均采用光滑样条逼近。为增强方法的稳定性，我们引入了一个基于高阶人工扩散线性组合的稳定化项。该稳定化项的设计旨在使线性系统成为下块三角矩阵，即在时间维度上呈下三角形式。为保持最优精度，进一步根据残差对稳定化项进行加权。通过一系列数值实验，我们验证了该方法的能力，展示了其稳定性和精度。