Optimal order finite element approximations for variable-order time-fractional diffusion equations

2019/05/14 by Xiangcheng Zheng, Zheng, Xiangcheng, Fanhai Zeng +3
Mathematics · #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1905.05732

openalex publication_date 2019/05/14 · openalex created_date 2019/05/29 · openalex updated_date 2026/07/28

Abstract

We study a fully discrete finite element method for variable-order time-fractional diffusion equations with a time-dependent variable order. Optimal convergence estimates are proved with the first-order accuracy in time (and second order accuracy in space) under the uniform or graded temporal mesh without full regularity assumptions of the solutions. Numerical experiments are presented to substantiate the analysis.

Citations

• Fractional Differential Equations

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