Unconditional convergence and optimal error estimates of a Galerkin-mixed FEM for incompressible miscible flow in porous media

Buyang Li, Weiwei Sun

Research output: Journal article publicationJournal articleAcademic researchpeer-review

107 Citations (Scopus)

Abstract

In this paper, we study the unconditional convergence and error estimates of a Galerkin-mixed FEM with the linearized semi-implicit Euler scheme for the equations of incompressible miscible flow in porous media. We prove that the optimal L2error estimates hold without any time-step (convergence) conditions, while all previous works require certain time-step restrictions. Our theoretical results provide a new understanding on commonly used linearized schemes. The proof is based on a splitting of the error into two parts: the error from the time discretization of the PDEs and the error from the finite element discretization of corresponding time-discrete PDEs. The approach used in this paper can be applied to more general nonlinear parabolic systems and many other linearized (semi)-implicit time discretizations.
Original languageEnglish
Pages (from-to)1959-1977
Number of pages19
JournalSIAM Journal on Numerical Analysis
Volume51
Issue number4
DOIs
Publication statusPublished - 6 Dec 2013
Externally publishedYes

Keywords

  • Galerkin-mixed FEM
  • Incompressible miscible flow
  • Optimal error estimate
  • Unconditional stability

ASJC Scopus subject areas

  • Numerical Analysis

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