Unconditionally optimal error estimates of a linearized weak Galerkin finite element method for semilinear parabolic equations

Ying Liu, Zhen Guan, Yufeng Nie

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

In this paper, we consider the unconditionally optimal error estimates of the linearized backward Euler scheme with the weak Galerkin finite element method for semilinear parabolic equations. With the error splitting technique and elliptic projection, the optimal error estimates in L2-norm and the discrete H1-norm are derived without any restriction on the time stepsize. Numerical results on both polygonal and tetrahedral meshes are provided to illustrate our theoretical conclusions.

Original languageEnglish
Article number47
JournalAdvances in Computational Mathematics
Volume48
Issue number4
DOIs
StatePublished - Aug 2022

Keywords

  • Elliptic projection
  • Linearized backward Euler scheme
  • Semilinear parabolic equations
  • Unconditionally optimal error estimates
  • Weak Galerkin finite element method

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