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Robust approximation error estimates and multigrid solvers for isogeometric multi-patch discretizations
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DOI：10.1142/S021820251850046X.png)
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Abstract
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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 arising 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 B-spline patch. In computer aided design, such domains are typically represented as a union of multiple patches. In this paper, we extend - for two-dimensional domains - the approximation error estimates and the multigrid solver to this multi-patch case.
Keywords:
Isogeometric analysis
multi-patch domains
approximation errors
multigrid methods
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