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<p>In this paper, we explore a stable numerical scheme for solving the Maxwell-Cattaneo equation with discontinuous coefficients. The fully discrete scheme is constructed through a combination of a modified stable generalized finite element method (SGFEM) for spatial discretization and central finite difference formulas (CFDFs) for temporal discretization, which ensures optimal convergence and unconditional stability. The unconditional stability of the fully discrete scheme is demonstrated by applying generalized eigenvalue analysis technique. Finally, numerical experiments have verified the optimal convergence of our proposed numerical scheme in the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^{\infty}\)</EquationSource> </InlineEquation> and <i>L</i><sup>2</sup> norms, while also confirming its unconditional stability.</p>

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An unconditionally stable central finite difference formula in SGFEM for Maxwell-Cattaneo equation with an interface

  • 期刊论文

  • 发表日期：

    2026年2月9日

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  • Pengfei Zhu,
  • Kai Liu

摘要

In this paper, we explore a stable numerical scheme for solving the Maxwell-Cattaneo equation with discontinuous coefficients. The fully discrete scheme is constructed through a combination of a modified stable generalized finite element method (SGFEM) for spatial discretization and central finite difference formulas (CFDFs) for temporal discretization, which ensures optimal convergence and unconditional stability. The unconditional stability of the fully discrete scheme is demonstrated by applying generalized eigenvalue analysis technique. Finally, numerical experiments have verified the optimal convergence of our proposed numerical scheme in the \(L^{\infty}\) and L2 norms, while also confirming its unconditional stability.