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

• Published in: PloS one Vol. 18; no. 3; p. e0277126
• Main Authors: Hossain, Muhammad Shakhawat, Xiong, Chunguang, Sun, Huafei
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 30.03.2023; Public Library of Science (PLoS)
• Subjects: Adaptive algorithms; Algorithms; Analysis; Approximation; Computer and Information Sciences; Data mining; Differential equations; Engineering and Technology; Error analysis; Evaluation; Finite Element Analysis; Finite element method; Functions, Exponential; Galerkin method; Hypotheses; Mathematical functions; Methods; Numerical experiments; Parameters; Partial differential equations; Physical Sciences; Records; Reproducibility of Results; Research and Analysis Methods; China
• ISSN: 1932-6203; 1932-6203
• DOI: 10.1371/journal.pone.0277126

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.