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

Explicit time advancement for continuous finite elements requires theinversion of a global mass matrix. For spectral element simulations onquadrilaterals and hexahedra, there is an accurate approximate mass matrixwhich is diagonal, making it computationally efficient for explicitsimulations. In this article it is shown that for the standard space ofpolynomials used with triangular elements, denoted $\mathcal{T}(p)$ where $p$is the degree of the space, there is no diagonal approximate mass matrix thatpermits accurate solutions. Accuracy is defined as giving an exact projectionof functions in $\mathcal{T}(p-1)$. In light of this, a lower-triangularpseudo-mass matrix method is introduced and demonstrated for the space$\mathcal{T}(3)$. The pseudo-mass matrix and accompanying high-order basisallow for computationally efficient time-stepping techniques withoutsacrificing the accuracy of the spatial approximation for unstructuredtriangular meshes.

A High-Order Lower-Triangular Pseudo-Mass Matrix for Explicit Time Advancement of hp Triangular Finite Element Methods