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Numerical Algorithms
Erschienen in: Numerical Algorithms 1/2024

04.09.2023 | Original Paper

High order hybrid asymptotic augmented finite volume methods for nonlinear degenerate wave equations

verfasst von: Wenju Liu, Tengjin Zhao, Zhiyue Zhang

Erschienen in: Numerical Algorithms | Ausgabe 1/2024

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Abstract

In this paper, we provide high order hybrid asymptotic augmented finite volume schemes on a uniform grid for nonlinear weakly degenerate and strongly degenerate wave equations. The whole domain is divided into singular and regular subdomains by introducing an intermediate point. Puiseux series asymptotic technique is used in singular subdomain, and augmented numerical method is used in regular subdomain. The key to the method are the recovery of Puiseux series for the nonlinear degenerate wave equation in singular subdomain and the organic combination between the singular and regular subdomains by means of augmented variables related to singularity. In particular, through imposing a condition at the intermediate point, we can not only improve the accuracy of the augmented variables, but also avoid the restriction conditions when the mesh is divided in regular subdomain. The advantage of this method is that the global convergence order of the degenerate wave equation is determined by the augmented numerical scheme in regular subdomain. A rigorous error estimate is conducted for the solution of the degenerate wave equation. Numerical examples on weakly degenerate and strongly degenerate problems are provided to illustrate the effectiveness of the proposed method. Especially, we use the method to solve an interesting example of a degenerate wave equation with coefficient blow-up.
Vorheriger Artikel A multidimensional Hermite-Gauss sampling formula for analytic functions of several variables
Nächster Artikel Local and parallel multigrid method for semilinear Neumann problem with nonlinear boundary condition

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Metadaten
Titel
High order hybrid asymptotic augmented finite volume methods for nonlinear degenerate wave equations
verfasst von
Wenju Liu
Tengjin Zhao
Zhiyue Zhang
Publikationsdatum
04.09.2023
Verlag
Springer US
Erschienen in
Numerical Algorithms / Ausgabe 1/2024
Print ISSN: 1017-1398
Elektronische ISSN: 1572-9265
DOI
https://doi.org/10.1007/s11075-023-01642-6

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