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A mixed virtual element method for the time-fractional fourth-order subdiffusion equation

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Abstract

We propose and analyze a mixed virtual element method for time-fractional fourth-order subdiffusion equation involving the Caputo fractional derivative on polygonal meshes, whose solutions display a typical weak singularity at the initial time. By introducing an auxiliary variable σ = Δu, then the fourth-order equation can be split into the coupled system of two second-order equations. Based on the L1 scheme on a graded temporal mesh, the unconditional stability of the fully discrete is proved for two variables; and the priori error estimates are derived in L2 norm for the scalar unknown u and the variable σ, respectively. Moreover, the priori error result in H1 semi-norm for the scalar unknown u also is obtained. Finally, a numerical calculation is implemented to verify the theoretical results.

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Funding

This paper is supported by National Nature Science Foundation of China (Nos. 11971337, 11971416)

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Authors and Affiliations

  1. School of Mathematics, Sichuan University, Chengdu, 610064, China

    Yadong Zhang & Minfu Feng

  2. School of Science, Xuchang University, 461000, Xuchang, China

    Yadong Zhang

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  1. Yadong Zhang
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  2. Minfu Feng
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Correspondence to Minfu Feng.

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Zhang, Y., Feng, M. A mixed virtual element method for the time-fractional fourth-order subdiffusion equation. Numer Algor 90, 1617–1637 (2022). https://doi.org/10.1007/s11075-021-01244-0

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