Unconditionally optimal convergence of an energy-conserving and linearly implicit scheme for nonlinear wave equations

Waixiang Cao; Dongfang Li; Zhimin Zhang

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arXiv · 2103.04700

Unconditionally optimal convergence of an energy-conserving and linearly implicit scheme for nonlinear wave equations

Waixiang Cao·Dongfang Li·Zhimin Zhang

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Abstract

In this paper, we present and analyze an energy-conserving and linearly implicit scheme for solving the nonlinear wave equations. Optimal error estimates in time and superconvergent error estimates in space are established without time-step dependent on the spatial mesh size. The key is to estimate directly the solution bounds in the $H^2$-norm for both the nonlinear wave equation and the corresponding fully discrete scheme, while the previous investigations rely on the temporal-spatial error splitting approach. Numerical examples are presented to confirm energy-conserving properties, unconditional convergence, and optimal error estimates, respectively, of the proposed fully discrete schemes.

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BibTeX RIS

Waixiang Cao, Dongfang Li, Zhimin Zhang. 2021-03-08. Unconditionally optimal convergence of an energy-conserving and linearly implicit scheme for nonlinear wave equations. https://arxiv.org/abs/2103.04700

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