Subdiffusion with a time-dependent coefficient: Analysis and numerical solution

Bangti Jin, Buyang Li, Zhi Zhou

Research output: Journal article publicationJournal articleAcademic researchpeer-review

23 Citations (Scopus)

Abstract

In this work, a complete error analysis is presented for fully discrete solutions of the subdiffusion equation with a time-dependent diffusion coefficient, obtained by the Galerkin finite element method with conforming piecewise linear finite elements in space and backward Euler convolution quadrature in time. The regularity of the solutions of the subdiffusion model is proved for both nonsmooth initial data and incompatible source term. Optimal-order convergence of the numerical solutions is established using the proven solution regularity and a novel perturbation argument via freezing the diffusion coefficient at a fixed time. The analysis is supported by numerical experiments.

Original languageEnglish
Pages (from-to)2157-2186
Number of pages30
JournalMathematics of Computation
Volume88
Issue number319
DOIs
Publication statusPublished - Sep 2019

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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