| Title | Analysis and numerical approximation to time-fractional diffusion equation with a general time-dependent variable order |
| Authors | Zheng, Xiangcheng Wang, Hong |
| Affiliation | Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China Univ South Carolina, Dept Math, Columbia, SC 29208 USA |
| Keywords | ANOMALOUS DIFFUSION DISCRETIZATION REGULARITY SCHEMES MODELS |
| Issue Date | May-2021 |
| Publisher | NONLINEAR DYNAMICS |
| Abstract | Variable-order time-fractional diffusion equations (tFDEs), in which the variable fractional order accommodates the fractal dimension change of the surrounding medium via the Hurst index, provide a competitive instrument to describe anomalously diffusive transport of particles through deformable heterogeneous materials. We analyze the mapping properties of the fractional integral with a general time-dependent variable order, based on which we prove the well-posedness and smoothing properties of corresponding variable-order tFDE model in multiple space dimensions. We then derive and analyze a fully discretized finite element approximation, in which we develop a novel decomposition of L-1 discretization coefficients to prove an optimal-order error estimate of the numerical scheme based only on the regularity assumptions on the data. Numerical experiments are performed to substantiate the theoretical findings. |
| URI | http://hdl.handle.net/20.500.11897/614319 |
| ISSN | 0924-090X |
| DOI | 10.1007/s11071-021-06353-y |
| Indexed | EI SCI(E) |
| Appears in Collections: | 数学科学学院 |
