A variational approach to the sum splitting scheme. (20th January 2021)

• Record Type: Journal Article
• Authors: Eisenmann, Monika; Hansen, Eskil
• Is Part Of: IMA journal of numerical analysis. Volume 42:Number 1(2022)
• Page Start: 923
• Page End: 950
• Publication Date: 2021-01-20
• Subjects: nonlinear evolution problem -- monotone operator -- operator splitting -- convergence; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/draa100
• Languages: English
• ISSNs: 0272-4979

Abstract

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.