Spatial and Temporal Discretizations Using Totally Volume Integrals Discontinuous-Galerkin Methods: Application to Non-Standard Interval [0, √π]

Authors: Elhadi I. Elhadi A, Ayad A. Abdalla, Esam A. Alabeedy

Abstract:

This study is part of a series of research papers investigating shape functions for non-standard intervals (i.e. intervals other than the standard [0, 1] or [-1, 1]) within the Totally Volume Integrals Discontinuous-Galerkin (TVI-DG) framework. In this paper, the shape functions for the interval [0, √π] are explored. The numerical results confirm that the shape functions constructed from polynomials within [0, √π] achieve the expected order of accuracy. Furthermore, a comparison between the shape functions for [0, √π] and those for the standard interval [0,1] demonstrates their equivalence in numerical results at T=√π.

Keywords: Discontinuous-Galerkin, Non-standard interval, shape function, Totally Volume Integrals.

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