Robust approximation error estimates and multigrid solvers for isogeometric multi-patch discretizations
Abstract
In recent publications, the author and his coworkers have shown robust approximation error estimates for B-splines of maximum smoothness and have proposed multigrid methods based on them. These methods allow to solve the linear system arizing from the discretization of a partial differential equation in Isogeometric Analysis in a single-patch setting with convergence rates that are provably robust both in the grid size and the spline degree. In real-world problems, the computational domain cannot be nicely represented by just one patch. In computer aided design, such domains are typically represented as a union of multiple patches. In the present paper, we extend the approximation error estimates and the multigrid solver to this multi-patch case.
Cite
@article{arxiv.1709.05375,
title = {Robust approximation error estimates and multigrid solvers for isogeometric multi-patch discretizations},
author = {Stefan Takacs},
journal= {arXiv preprint arXiv:1709.05375},
year = {2021}
}