标题： 稳定化等几何配置方法用于标量输运和不可压缩流体流动 显示英文标题

标题： Stabilized Isogeometric Collocation Methods For Scalar Transport and Incompressible Fluid Flow

摘要： 在这项工作中，我们将经典的基于残差的稳定化技术推广到样条配置设定中。受到流线迎风 Petrov-Galerkin 和压力稳定 Petrov-Galerkin 方法的启发，我们提出的稳定化配置方案解决了由于对流和压力不稳定可能产生的虚假振荡问题。数值算例（包括对流扩散方程、Stokes 方程和不可压缩 Navier-Stokes 方程）表明，所提出的稳定化格式在保持标准光滑问题下高阶收敛率和精度的同时，展现了良好的有效性。 显示英文摘要

摘要： 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.