A mixed variational inequality method for solving Signorini problems. (February 2023) - Cheng, Yongfeng
Abstract: This paper presents a new iterative method for solving Signorini problems. Boundary integral equations are established by discretizing the boundary of the problem, and the system equations related only to the unknown variables on the boundary of the problem are derived. Then, the Signorini boundary conditions of the problem are expressed as equivalent variational inequalities. By considering a simultaneous system of equations and variational inequalities, the Signorini problem is reduced to a mixed variational inequality problem. Finally, a compatibility iteration algorithm for solving mixed variational inequalities is designed based on the projection-contraction algorithm. Several examples are tested to demonstrate the accuracy and effectiveness of the proposed algorithm.