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 main purpose of this paper is to describe a space-time discontinuous Galerin (DG) method based on an extended space-time approximation space for the linear first order hyperbolic equation that contains a high frequency component. We extend the space-time DG spaces of tensor-product of polynomials by adding trigonometric functions in space and time that capture the oscillatory behavior of the solution. We construct the method by combining the basic framework of the space-time DG method with the extended finite element method. The basic principle of the method is integrating the features of the partial differential equation with the standard space-time spaces in the approximation. We present error analysis of the space-time DG method for the linear first order hyperbolic problems. We show that the new space-time DG approximation has an improvement in the convergence compared to the space-time DG schemes with tensor-product polynomials. Numerical examples verify the theoretical findings and demonstrate the effects of the proposed method.

A space-time discontinuous Galerkin method for linear hyperbolic PDE's with high frequencies