Maximal Lerror analysis of FEMs for nonlinear parabolic equations with nonsmooth coefficients

Buyang Li, Weiwei Sun

Research output: Journal article publicationJournal articleAcademic researchpeer-review

4 Citations (Scopus)

Abstract

The paper is concerned with Lperror analysis of semi-discrete Galerkin FEMs for nonlinear parabolic equations. The classical energy approach relies heavily on the strong regularity assumption of the diffusion coefficient, which may not be satisfied in many physical applications. Here we focus our attention on a general nonlinear parabolic equation (or system) in a convex polygon or polyhedron with a nonlinear and Lipschitz continuous diffusion coefficient. We first establish the discrete maximal Lp-regularity for a linear parabolic equation with time-dependent diffusion coefficients in L∞(0, T; W1,N+ϵ) ∩ C(Ω × [0, T ]) for some ϵ > 0, where N denotes the dimension of the domain, while previous analyses were restricted to the problem with certain stronger regularity assumption. With the proved discrete maximal Lp-regularity, we then establish an optimal Lperror estimate and an almost optimal L∞error estimate of the finite element solution for the nonlinear parabolic equation.
Original languageEnglish
Pages (from-to)670-687
Number of pages18
JournalInternational Journal of Numerical Analysis and Modeling
Volume14
Issue number4-5
Publication statusPublished - 1 Jan 2017

Keywords

  • Finite element method
  • Maximal L -regularity p
  • Nonlinear parabolic equation
  • Nonsmooth coefficients
  • Optimal error estimate
  • Polyhedron

ASJC Scopus subject areas

  • Numerical Analysis

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