A priori and a posteriori error analysis of the first order hyperbolic equation by using DG method

Muhammad Shakhawat Hossain, Chunguang Xiong and Huafei Sun

PLOS ONE, 2023, vol. 18, issue 3, 1-23

Abstract: In this research article, a discontinuous Galerkin method with a weighted parameter θ and a penalty parameter γ is proposed for solving the first order hyperbolic equation. The key aim of this method is to design an error estimation for both a priori and a posteriori error analysis on general finite element meshes. It is also exposed to the reliability and effectiveness of both parameters in the order of convergence of the solutions. For a posteriori error estimation, residual adaptive mesh- refining algorithm is employed. A series of numerical experiments are illustrated that demonstrate the efficiency of the method.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:plo:pone00:0277126

DOI: 10.1371/journal.pone.0277126

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