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<p>In this paper, we study a numerical method for solving the time-fractional Allen-Cahn equation. A fully discrete scheme is developed using an ultra-weak discontinuous Galerkin method for spatial discretization, and the temporal discretization is performed using the <i>L</i>1 method on graded meshes. A rigorous theoretical analysis is presented, establishing unique solvability, energy stability, and optimal <i>a priori</i> error estimates. The efficiency of the proposed scheme is demonstrated through numerical examples. Additionally, key physical properties such as the energy dissipation law, maximum principle, phase separation, and coalescence phenomena are investigated through simulations.</p>

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Ultra-weak discontinuous Galerkin method for time-fractional Allen-Cahn equation

  • 期刊论文

  • 发表日期：

    2026年4月29日

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  • Deeksha Singh,
  • Rajen Kumar Sinha

摘要

In this paper, we study a numerical method for solving the time-fractional Allen-Cahn equation. A fully discrete scheme is developed using an ultra-weak discontinuous Galerkin method for spatial discretization, and the temporal discretization is performed using the L1 method on graded meshes. A rigorous theoretical analysis is presented, establishing unique solvability, energy stability, and optimal a priori error estimates. The efficiency of the proposed scheme is demonstrated through numerical examples. Additionally, key physical properties such as the energy dissipation law, maximum principle, phase separation, and coalescence phenomena are investigated through simulations.