Stability and convergence analysis of the mixed finite element method for subdiffusive Oseen equations

Zhen Wang, Yujie Wang and Rui Zhu

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 245, issue C, 483-511

Abstract: This paper focuses on developing efficient numerical schemes for the subdiffusive Oseen equations with Caputo time-fractional derivative of order α∈(0,1). To address the computational challenges posed by the non-locality of the fractional derivative, we propose two distinct numerical methods, both employing mixed finite element methods for spatial discretization. Firstly, a variable-step fast L1 formula is introduced for time discretization, significantly reducing computational cost and memory requirements. The stability and convergence of this scheme are rigorously analyzed using a discrete Gronwall inequality, leading to optimal error estimates and verification of its energy stability. Secondly, a higher-accuracy uniform-step L1-2-3 formula is applied for time discretization, while the spatial direction is discretized via the mixed finite element method, with the stability and convergence of the scheme also demonstrated analytically. Finally, a series of numerical experiments are conducted to confirm the algorithms’ efficiency, convergence rates, and the validity of the theoretical findings, demonstrating their superior performance for solving fractional subdiffusion problems.

Keywords: Subdiffusive Oseen equations; Mixed finite element method; Fast L1 formula; L1-2-3 formula; Stability and convergence (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:245:y:2026:i:c:p:483-511

DOI: 10.1016/j.matcom.2026.01.024

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