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}
}