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 discuss computing with hierarchies of families of (potentially weighted)semiclassical Jacobi polynomials which arise in the construction ofmultivariate orthogonal polynomials. In particular, we outline how to buildconnection and differentiation matrices with optimal complexity and computeanalysis and synthesis operations in quasi-optimal complexity. We investigate aparticular application of these results to constructing orthogonal polynomialsin annuli, called the generalised Zernike annular polynomials, which lead tosparse discretisations of partial differential equations. We compare against ascaled-and-shifted Chebyshev--Fourier series showing that in general theannular polynomials converge faster when approximating smooth functions andhave better conditioning. We also construct a sparse spectral element method bycombining disk and annulus cells, which is highly effective for solving PDEswith radially discontinuous variable coefficients and data.

Building hierarchies of semiclassical Jacobi polynomials for spectral methods in annuli