A variational approach to the sum splitting scheme

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Abstract

Nonlinear parabolic equations are frequently encountered in applications and efficient approximating techniques for their solution are of great importance. In order to provide an effective scheme for the temporal approximation of such equations, we present a sum splitting scheme that comes with a straightforward parallelization strategy. The convergence analysis is carried out in a variational framework that allows for a general setting and, in particular, nontrivial temporal coefficients. The aim of this work is to illustrate the significant advantages of a variational framework for operator splittings and to use this to extend semigroup-based theory for this type of scheme.


Original languageEnglish
Pages (from-to)923-950
JournalIMA Journal of Numerical Analysis
Volume42
Issue number1
DOIs
Publication statusPublished - 2022 Jan 20

Subject classification (UKÄ)

  • Computational Mathematics

Free keywords

  • Nonlinear evolution problem
  • monotone operator
  • operator splitting
  • convergence

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