English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We derive bounds for the minimum and maximum eigenvalues and the spectralcondition number of matrices for isogeometric discretizations of ellipticpartial differential equations in an open, bounded, simply connected Lipschitzdomain $\Omega\subset \mathbb{R}^d$, $d\in\{2,3\}$. We consider refinementsbased on mesh size $h$ and polynomial degree $p$ with maximum regularity ofspline basis functions. For the $h$-refinement, the condition number of thestiffness matrix is bounded above by a constant times $ h^{-2}$ and thecondition number of the mass matrix is uniformly bounded. For the$p$-refinement, the condition number grows exponentially and is bounded aboveby $p^{2d+2}4^{pd}$ and $p^{2d}4^{pd}$ for the stiffness and mass matrices,respectively. Rigorous theoretical proofs of these estimates and supportingnumerical results are provided.

Condition number estimates for matrices arising in NURBS based isogeometric discretizations of elliptic partial differential equations