An analysis of galerkin proper orthogonal decomposition for subdiffusion

Bangti Jin, Zhi Zhou

Research output: Journal article publicationJournal articleAcademic researchpeer-review

19 Citations (Scopus)

Abstract

In this work, we develop a novel Galerkin-L1-POD scheme for the subdiffusion model with a Caputo fractional derivative of order α ϵ (0,1) in time, which is often used to describe anomalous diffusion processes in heterogeneous media. The nonlocality of the fractional derivative requires storing all the solutions from time zero. The proposed scheme is based on continuous piecewise linear finite elements, L1 time stepping, and proper orthogonal decomposition (POD). By constructing an effective reduced-order model using problem-adapted basis functions, it can significantly reduce the computational complexity and storage requirement. We shall provide a complete error analysis of the scheme under realistic regularity assumptions by means of a novel energy argument. Extensive numerical experiments are presented to verify the convergence analysis and the efficiency of the proposed scheme.
Original languageEnglish
Pages (from-to)89-113
Number of pages25
JournalESAIM: Mathematical Modelling and Numerical Analysis
Volume51
Issue number1
DOIs
Publication statusPublished - 1 Jan 2017
Externally publishedYes

Keywords

  • Energy argument
  • Error estimates
  • Fractional diffusion
  • Proper orthogonal decomposition

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics

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