English

Stabilized Isogeometric Collocation Methods For Scalar Transport and Incompressible Fluid Flow

Numerical Analysis 2023-06-02 v1 Numerical Analysis

Abstract

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.

Keywords

Cite

@article{arxiv.2306.00601,
  title  = {Stabilized Isogeometric Collocation Methods For Scalar Transport and Incompressible Fluid Flow},
  author = {Ryan M. Aronson and Corey Wetterer-Nelson and John A. Evans},
  journal= {arXiv preprint arXiv:2306.00601},
  year   = {2023}
}
R2 v1 2026-06-28T10:53:14.079Z