Duality RBF-PS Method For Elliptic Variational Inequality

Elastoplastic torsion problem and Bingham fluid problem in the cylindrical pipe appear widely in the fields of physics, mechanics, engineering, etc. These problems can be often formulated as elliptic variational inequality. In this paper, we propose the coupling of a duality method based on Yosida approximation and RBF-PS method, and apply the coupling method to the elastoplatic torsion problem and Bingham fluid problem in the cylindrical pipe.The main work is as follows:1. In chapter2, it introduces RBF-PS method and its application in the differential equations in brief. Numerical examples show the validity of this method. It presents a duality method based on Yosida approximation and its application in elliptic variational inequality problems in detail. So we present two new algorithms to solve variational inequality problems.2. In chapter3, firstly, we give the basic model of the elastoplastic torsion problem and the mathematical description of the first kind of elliptic variational inequality. Secondly, we construct the coupling method of a duality method based on Yosida approximation and RBF-PS method. Finally, we compute some numerical examples in one-dimensional and two-dimensional region. By comparison with the RBF-PS method, it verifies the validity of this method, and show that new method have the advantage of easily programming, implementing, small amount of calculation and no need of any mesh.3. In chapter4, we introduce the basic model and the second kind of elliptic variational inequality of the Bingham fluid problem in the cylindrical pipe. And then we construct the coupling method of a duality method based on Yosida approximation and RBF-PS method. Numerical examples illustrates the effectiveness and precision of our method. 4. In chapter5, the conclusion and the prospect for future work are given.