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

Finite difference method and pseudo-spectral method have been widely used inthe numerical relativity to solve the Einstein equations. As the third majorcategory method to solve partial differential equations, finite element methodis much less used in numerical relativity. In this paper we design a finiteelement algorithm to solve the evolution part of the Einstein equations. Thispaper is the second one of a systematic investigation of applying adaptivefinite element method to the Einstein equations, especially aim for binarycompact objects simulations. The first paper of this series has beencontributed to the constrained part of the Einstein equations for initial data.Since applying finite element method to the Einstein equations is a bigproject, we mainly propose the theoretical framework of a finite elementalgorithm together with local discontinuous Galerkin method for the Einsteinequations in the current work. In addition, we have tested our algorithm basedon the spherical symmetric spacetime evolution. In order to simplify ournumerical tests, we have reduced the problem to a one-dimensional space problemby taking the advantage of the spherical symmetry. Our reduced equation systemis a new formalism for spherical symmetric spacetime simulation. Based on ourtest results, we find that our finite element method can capture the shockformation which is introduced by numerical error. In contrast, such shock issmoothed out by numerical dissipation within the finite difference method. Wesuspect this is the part reason for that the accuracy of finite element methodis higher than finite difference method. At the same time kinds of formulationparameters setting are also discussed.

Binary black hole simulation with an adaptive finite element method II: Application of local discontinuous Galerkin method to Einstein equations