Discontinuous Galerkin discretization in time of systems of second-order nonlinear hyperbolic equations

Shao, Aili

doi:10.1051/m2an/2022066

Shao, Aili

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 56 (2022) no. 6, pp. 2255-2296

Résumé

In this paper we study the finite element approximation of systems of second-order nonlinear hyperbolic equations. The proposed numerical method combines a hp-version discontinuous Galerkin finite element approximation in the time direction with an H¹(Ω)-conforming finite element approximation in the spatial variables. Error bounds at the temporal nodal points are derived under a weak restriction on the temporal step size in terms of the spatial mesh size. Numerical experiments are presented to verify the theoretical results.

MR Zbl

DOI : 10.1051/m2an/2022066

Classification : 65M60, 65M12, 35L72, 35L53
Keywords: Numerical analysis, finite element method, discontinuous Galerkin method, second-order nonlinear hyperbolic PDEs, nonlinear systems of PDEs, nonlinear elastodynamics equations

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     author = {Shao, Aili},
     title = {Discontinuous {Galerkin} discretization in time of systems of second-order nonlinear hyperbolic equations},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {2255--2296},
     year = {2022},
     publisher = {EDP-Sciences},
     volume = {56},
     number = {6},
     doi = {10.1051/m2an/2022066},
     mrnumber = {4519224},
     zbl = {1522.65178},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/m2an/2022066/}
}

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Shao, Aili. Discontinuous Galerkin discretization in time of systems of second-order nonlinear hyperbolic equations. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 56 (2022) no. 6, pp. 2255-2296. doi: 10.1051/m2an/2022066

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