Galerkin Type Methods for Semilinear Time-Fractional Diffusion Problems

Samir Karaa*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We derive optimal L2-error estimates for semilinear time-fractional subdiffusion problems involving Caputo derivatives in time of order α∈ (0 , 1) , for cases with smooth and nonsmooth initial data. A general framework is introduced allowing a unified error analysis of Galerkin type space approximation methods. The analysis is based on a semigroup type approach and exploits the properties of the inverse of the associated elliptic operator. Completely discrete schemes are analyzed in the same framework using a backward Euler convolution quadrature method in time. Numerical examples including conforming, nonconforming and mixed finite element methods are presented to illustrate the theoretical results.

Original languageEnglish
Article number46
JournalJournal of Scientific Computing
Volume83
Issue number3
DOIs
Publication statusPublished - Jun 1 2020
Externally publishedYes

Keywords

  • Convolution quadrature
  • Error estimate
  • Galerkin method
  • Mixed FE method
  • Nonconforming FE method
  • Semilinear fractional diffusion

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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