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

doi:10.1007/s42967-023-00301-w

Abstract

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 H¹-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.

Key words: Unconditionally superconvergence error estimate, Nonlinear wave equation, Linearized energy-stable scalar auxiliary variable (SAV) Galerkin scheme

CLC Number:

Huaijun Yang. Unconditionally Superconvergence Error Analysis of an Energy-Stable and Linearized Galerkin Finite Element Method for Nonlinear Wave Equations[J]. Communications on Applied Mathematics and Computation, 2025, 7(4): 1264-1281.

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

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