# A variational approach to the sum splitting scheme

## TL;DR

This paper introduces a variational sum splitting scheme for nonlinear parabolic equations, enabling efficient parallel computation and broad applicability through a general convergence analysis.

## Contribution

It presents a novel variational framework for sum splitting schemes, extending semigroup theory and accommodating complex temporal coefficients.

## Key findings

- Scheme allows straightforward parallelization
- Convergence analysis in a general variational setting
- Applicable to equations with nontrivial temporal coefficients

## 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 straight forward 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 use this to extend semigroup based theory for this type of scheme.