Abstract
We propose a projection iterative algorithm based on a fixed point equation for solving a certain class of Signorini problem. The satisfaction of the Signorini boundary conditions is verified in a projection iterative manner, and at each iterative step, an elliptic mixed boundary value problem is solved by a boundary element method which is suitable for any domain. We prove the convergence of the algorithm by the property of projection. The advantage of this algorithm is that it is easy to be implemented and converge quickly. Some numerical results show the accuracy and effectiveness of the algorithm.
Highlights
Domain discretization methods such as the finite element method (FEM) and the finite differential method (FDM) have been extensively applied for the numerical solution of Signorini problems [1,2,3,4,5]
Signorini problems for the Laplace equation are solved by a decomposition–coordination method (DCM) in [19], which is based on boundary variational inequality formulations
The boundary element-linear complementary method (BE-LCM) has been employed to solve Signorini problems, and a projected successive over-relaxation iterative method is applied to the problem effectively in [20]
Summary
Domain discretization methods such as the finite element method (FEM) and the finite differential method (FDM) have been extensively applied for the numerical solution of Signorini problems [1,2,3,4,5]. These methods require the discretization of entire domain which results in high computational cost. Signorini problems for the Laplace equation are solved by a decomposition–coordination method (DCM) in [19], which is based on boundary variational inequality formulations.
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