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

The purpose of this paper is to discuss representations of high order $C^0$finite element spaces on simplicial meshes in any dimension. When computingwith high order piecewise polynomials the conditioning of the basis is likelyto be important. The main result of this paper is a construction ofrepresentations by frames such that the associated $L^2$ condition number isbounded independently of the polynomial degree. To our knowledge, such arepresentation has not been presented earlier. The main tools we will use forthe construction is the bubble transform, introduced previously in [Falk andWinther, Found Comput Math (2016) 16: 297], and properties of Jacobipolynomials on simplexes in higher dimensions. We also include a briefdiscussion of preconditioned iterative methods for the finite element systemsin the setting of representations by frames.

Well-conditioned frames for high order finite element methods