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.

翻译：我们建议对热方程采用等离子测量空间时间方法,在时空均匀的样条近似值。在加勒金配方中添加一个基于高顺序人工扩散线性组合的稳定值。该词的设计是为了使线性系统在时间上保持三角形,扩展传统的更新概念。为了保持最佳的准确性,稳定值是在当地加权和完全激活的,以非线性的方式检测出尖锐层。我们进行数字测试,评估方法的稳定性和准确性。