Robust approximation error estimates and multigrid solvers for isogeometric multi-patch discretizations

Dr. Stefan Takacs

Oct. 17, 2017, 3:30 p.m. S2 416-1

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 presented paper, we extend the approximation error
estimates and the multigrid solver to this multi-patch case.