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Domain decomposition methods are a set of widely used tools forparallelization of partial differential equation solvers. Convergence is wellstudied for elliptic equations, but in the case of parabolic equations thereare hardly any results for general Lipschitz domains in two or more dimensions.The aim of this work is therefore to construct a new framework for analyzingnonoverlapping domain decomposition methods for the heat equation in aspace-time Lipschitz cylinder. The framework is based on a variationalformulation, inspired by recent studies of space-time finite elements usingSobolev spaces with fractional time regularity. In this framework, thetime-dependent Steklov--Poincar\'e operators are introduced and their essentialproperties are proven. We then derive the interface interpretations of theDirichlet--Neumann, Neumann--Neumann and Robin--Robin methods and show thatthese methods are well defined. Finally, we prove convergence of theRobin--Robin method and introduce a modified method with stronger convergenceproperties.

Time-dependent Steklov--Poincar\'e operators and space-time Robin--Robin decomposition for the heat equation