Adaptivity with dynamic meshes for space-time finite element discretizations of parabolic equations

Michael Schmich, Boris Vexler

Research output: Contribution to journalArticlepeer-review

109 Scopus citations

Abstract

In this paper, we develop an error estimator and an adaptive algorithm for efficient solution of parabolic partial differential equations. The error estimator assesses the discretization error with respect to a given quantity of physical interest and separates the influence of the time and space discretizations. This allows us to set up an efficient adaptive strategy producing economical (locally) refined meshes for each time step and an adapted time discretization. The space and time discretization errors are equilibrated, leading to an efficient method.

Original languageEnglish
Pages (from-to)369-393
Number of pages25
JournalSIAM Journal on Scientific Computing
Volume30
Issue number1
DOIs
StatePublished - 2007
Externally publishedYes

Keywords

  • A posteriori error estimation
  • Dynamic meshes
  • Mesh refinement
  • Parabolic equations
  • Space-time finite elements

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