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/

Zendy Plus

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

Zendy Tools

Zendy Open

In this paper we develop an $H^m$-conforming ($m\ge1$) spectral elementmethod on multi-dimensional domain associated with the partition intomulti-dimensional rectangles. We construct a set of basis functions on theinterval $[-1,1]$ that is made up of the generalized Jacobi polynomials (GJPs)and the nodal basis functions. So the basis functions on multi-dimensionalrectangles consist of the tensorial product of the basis functions on theinterval $[-1,1]$. Then we construct the spectral element interpolationoperator and prove the associated interpolation error estimates. Finally weapply the $H^2$-conforming spectral element method to the Helmholtztransmission eigenvalues that is a hot topic in the field engineering andmathematics.

An $H^m$-conforming spectral element method on multi-dimensional domain and its application to transmission eigenvalues