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arXiv · 2606.28443

A New $L2-1_σ$-Interior Penalty Method for Variable-Order Time-Fractional Subdiffusion Interface Problem with Curved Interface

Hongying Huang·Chanchan Hao·Changmu Yu·Huili Zhang
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Abstract

This paper treats variable-order time-fractional subdiffusion with discontinuous coefficients across a curved interface using $L2\!-\!1_σ$ time stepping on graded meshes and a symmetric interior penalty FEM on body-fitted meshes. Stability and optimal a priori error estimates in a discrete-in-time $L^2$ norm are established, yielding second-order temporal accuracy. While analysis typically assumes $α_n$ at $t_{n-σ_n}$ lies in the range of $α(t)$ on $[t_{n-1},t_n]$ and $α_n\le α(t_{n-α_n/2})$, experiments indicate the second inequality can be relaxed or omitted, enabling straightforward selection of $α_n$ from many admissible values without solving a nonlinear equation. Numerical results verify temporal rates $\min\{2,rδ\}$, spatial order $\min\{s,k+1\}$, and robustness to superconvergent points and interface geometry.

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Hongying Huang, Chanchan Hao, Changmu Yu, Huili Zhang. 2026-06-26. A New $L2-1_σ$-Interior Penalty Method for Variable-Order Time-Fractional Subdiffusion Interface Problem with Curved Interface. https://arxiv.org/abs/2606.28443

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