Error Analysis of Mixed Finite Element Methods for Nonlinear Parabolic Equations

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Original languageEnglish
Pages (from-to)1660-1678
Journal / PublicationJournal of Scientific Computing
Issue number3
Online published23 Jan 2018
Publication statusPublished - Dec 2018


In this paper, we prove a discrete embedding inequality for the Raviart–Thomas mixed finite element methods for second order elliptic equations, which is analogous to the Sobolev embedding inequality in the continuous setting. Then, by using the proved discrete embedding inequality, we provide an optimal error estimate for linearized mixed finite element methods for nonlinear parabolic equations. Several numerical examples are provided to confirm the theoretical analysis.

Research Area(s)

  • Discrete Sobolev embedding inequality, Finite element method, Nonlinear parabolic equations, Optimal error analysis, Unconditional convergence