文章基本信息

标题：An expanded mixed finite element simulation for two-sided time-dependent fractional diffusion problem
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作者：Qiong Yuan ; Huanzhen Chen
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2018
卷号：2018
期号：1
页码：34
DOI：10.1186/s13662-018-1483-4
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this paper, we consider a time-dependent diffusion problem with two-sided Riemann-Liouville fractional derivatives. By introducing a fractional-order flux as auxiliary variable, we establish the saddle-point variational formulation, based on which we employ a locally conservative mixed finite element method to approximate the unknown function, its derivative and the fractional flux in space and use the backward Euler scheme to discrete the time derivative, and thus propose a fully discrete expanded mixed finite element procedure. We prove the well-posedness and the optimal order error estimates of the proposed procedure for a sufficiently smooth solution. Numerical experiments are presented to confirm our theoretical findings.
关键词：time-dependent fractional diffusion problem ; expanded mixed finite element method ; fully discrete scheme ; well-posedness ; error estimates