Non-overlapping domain decomposition method for a variational inequality with gradient constraints

A Lapin,E Laitinen,S Lapin

doi:10.1088/1757-899x/158/1/012060

Abstract

Non-overlapping domain decomposition method is applied to a variational inequality with nonlinear diffusion-convection operator and gradient constraints. The method is based on the initial approximation of the problem and its subsequent splitting into subproblems. For the resulting constrained saddle point problem block relaxation-Uzawa iterative solution method is applied.

Highlights

Domain decomposition methods for the variational inequalities have been investigated for a long time
In this article we apply the aforementioned results on the iterative solution methods for the constrained saddle point problems to non-overlapping domain decomposition method for variational inequalities with gradient constraints
The proof is based on the theory of variational inequalities with monotone operators [19]

Summary

Introduction

Domain decomposition methods for the variational inequalities have been investigated for a long time. In [17] a generalization of this result for wider class of saddle point problems and for so-called block relaxation-Uzawa iterative solution method have been investigated. These results were applied to iterative solution methods for mesh variational inequalities with gradient constraints and for mesh approximations of state and control constrained optimal control problems in the numerous subsequent articles. In this article we apply the aforementioned results on the iterative solution methods for the constrained saddle point problems to non-overlapping domain decomposition method for variational inequalities with gradient constraints

Variational inequality and its approximation

Domain decomposition and constructing a saddle point problem m

A B w F