Consistency of the Douglas − Rachford Splitting Algorithm for the Sum of Three Nonlinear Operators: Application to the Stefan Problem in Permafrost Soils
Taras A. Dauzhenka · Applied and Computational Mathematics · 2013
Consistency of the Douglas – Rachford dimensional splitting scheme is proved for the sum of three nonlinear operators constituting an evolution equation. It is shown that the operators must be densely defined, maximal monotone and single valued on a real Hilbert space in order to satisfy conditions, under which the splitting algorithm can be applied. Numerical experiment conducted for a three-dimensional Stefan problem in permafrost soils suggests that the Douglas – Rachford scheme produces reasonable results, although the convergence rate remains unestablished.