A New Uzawa-exact Type Algorithm for Nonsymmetric Saddle Point Problems

TL;DR

This paper introduces a novel Uzawa-exact type algorithm designed specifically for nonsymmetric saddle point problems, with proven convergence and demonstrated effectiveness through numerical experiments.

Contribution

It presents a new Uzawa-exact algorithm tailored for nonsymmetric saddle point problems, expanding the toolkit for solving complex variational inequalities.

Findings

Convergence of the new algorithm is established.

Numerical experiments validate the algorithm's effectiveness.

Applicable to problems from Navier-Stokes discretization.

Abstract

Saddle point problems have been attracting people's attention in recent years. To solve large and sparse saddle point problems, Uzawa type algorithms were proposed. The main contribution of this paper is to present a new Uzawa-exact type algorithm from the aspect of optimization method to solve nonsymmetric saddle point problems, which often arise from linear variational inequalities and finite element discretization of Navier-Stokes equations. In the paper, convergence of the new algorithm is analysed and numerical experiments are presented.