A projection iterative algorithm for the Signorini problem using the boundary element method

This paper proposes a new iterative algorithm for the numerical solution of the Signorini problem for Laplacian using the boundary element method. Since the Signorini boundary conditions are equivalent to a projection fixed point problem, the Signorini boundary conditions can be transformed into a sequence of Dirichlet boundary conditions in a simple iterative manner. Therefore, the algorithm only requires solving a sequence of problems with straightforward boundary conditions. We also investigate the convergence criteria of the algorithm. As the iteration process is given on the Signorini boundary of the domain, the boundary element method is especially suitable for the algorithm. Finally, the numerical results demonstrate the accuracy and validity of the algorithm.