Unconditionally Superconvergence Error Analysis of an Energy-Stable and Linearized Galerkin Finite Element Method for Nonlinear Wave Equations

Abstract

In this paper, a linearized energy-stable scalar auxiliary variable (SAV) Galerkin scheme is investigated for a two-dimensional nonlinear wave equation and the unconditional superconvergence error estimates are obtained without any certain time-step restrictions. The key to the analysis is to derive the boundedness of the numerical solution in the

H^1

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-norm, which is different from the temporal-spatial error splitting approach used in the previous literature. Meanwhile, numerical results are provided to confirm the theoretical findings.

Keywords

Unconditionally superconvergence error estimate / Nonlinear wave equation / Linearized energy-stable scalar auxiliary variable (SAV) Galerkin scheme

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Funding

National Natural Science Foundation of China(12101568)

RIGHTS & PERMISSIONS

Shanghai University