A variational approach to the sum splitting scheme

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.

Automated summary

This paper introduces a sum splitting scheme for temporal approximation of nonlinear parabolic equations, with a straightforward parallelization strategy and convergence analysis in a variational framework. The focus is on illustrating the significant advantages of a variational framework for operator splittings and extending semigroup-based theory for this type of scheme.