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Analysis of a Full Discretization for a Fractional/Normal Diffusion Equation with Rough Dirichlet Boundary Data

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Abstract

This paper considers a fully discrete approximation of a fractional/normal diffusion equation with rough Dirichlet boundary data. The approximation uses the standard continuous piecewise linear element in space, and uses the L1 scheme in time. Nearly \( \alpha /4 \)-order temporal accuracy and nearly 1/2-order spatial accuracy are derived, where the spatial mesh size h and the time step \( \tau \) are independent. Numerical results are provided to confirm the theoretical results.

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Funding

This work was supported by National Natural Science Foundation of China (11901410, 11971337).

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Authors and Affiliations

  1. China West Normal University, Nanchong, 637002, China

    Qin Zhou

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

    Qin Zhou & Minfu Feng

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  1. Qin Zhou
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  2. Minfu Feng
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Correspondence to Minfu Feng.

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This work was supported by National Natural Science Foundation of China (11901410, 11971337)

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Zhou, Q., Feng, M. Analysis of a Full Discretization for a Fractional/Normal Diffusion Equation with Rough Dirichlet Boundary Data. J Sci Comput 92, 25 (2022). https://doi.org/10.1007/s10915-022-01875-y

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  • DOI: https://doi.org/10.1007/s10915-022-01875-y

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