In this work we adapt classical residual-based stabilization techniques to the spline collocation setting. Inspired by the Streamline-Upwind-Petrov-Galerkin and Pressure-Stabilizing-Petrov-Galerkin methods, our stabilized collocation schemes address spurious oscillations that can arise from advection and pressure instabilities. Numerical examples for the advection-diffusion equation, Stokes equations, and incompressible Navier-Stokes equations show the effectiveness of the proposed stabilized schemes while maintaining the high-order convergence rates and accuracy of standard isogeometric collocation on smooth problems.

翻译：本文针对样条配点框架，对经典残差基稳定化技术进行了适应性改进。受流线迎风Petrov-Galerkin方法与压力稳定化Petrov-Galerkin方法的启发，所提出的稳定化配点格式能够有效抑制由对流及压力不稳定性引发的虚假数值振荡。通过平流扩散方程、斯托克斯方程以及不可压缩纳维-斯托克斯方程的数值算例表明，所提稳定化方案在保持标准等几何配点法对光滑问题的高阶收敛精度与准确性的同时，验证了其有效性。