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<p>This paper presents a rigorous error analysis for a first-order, fully decoupled numerical scheme for the Ericksen-Leslie model of nematic liquid crystal flows, formulated within the scalar auxiliary variable (SAV) framework. The proposed scheme can be viewed as a simplified variant of the second-order PCSAV-ECT scheme introduced in our previous work [4], which has demonstrated excellent numerical stability and accuracy. Under suitable regularity assumptions, we establish optimal first-order error estimates for the velocity, director field and pressure. A key ingredient of the analysis is a discrete <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>∞</mi> </msup> </math></EquationSource> </InlineEquation>-bound of the director field, which allows effective control of the nonlinear coupling terms and facilitates the derivation of optimal error bounds.</p>

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A Priori Error Estimates of a First-Order Fully Decoupled SAV Scheme for the Ericksen-Leslie Model

  • 期刊论文

  • 发表日期：

    2026年7月9日

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  • Ruonan Cao,
  • Nianyu Yi

摘要

This paper presents a rigorous error analysis for a first-order, fully decoupled numerical scheme for the Ericksen-Leslie model of nematic liquid crystal flows, formulated within the scalar auxiliary variable (SAV) framework. The proposed scheme can be viewed as a simplified variant of the second-order PCSAV-ECT scheme introduced in our previous work [4], which has demonstrated excellent numerical stability and accuracy. Under suitable regularity assumptions, we establish optimal first-order error estimates for the velocity, director field and pressure. A key ingredient of the analysis is a discrete \(L^\infty \) L ∞ -bound of the director field, which allows effective control of the nonlinear coupling terms and facilitates the derivation of optimal error bounds.