The Boundary Element Method For Elliptic Unilateral Problems

In this paper, we consider the numerical approximations of elliptic unilateral problems. The boundary conditions of unilateral problems are nonlinear and complementary ones. As the complementary conditions lie on the boundary of the domain, BEM is very effective to solve them. Our purpose is to set up a new algorithm which is easy to solve the elliptic unilateral problems. Using the switching algorithm an unilateral problem is reacted as a bilateral problem. As known, the BEM is very effective in solving the bilateral problems. So a new algorithm, which is based on the BEM with the switching algorithm applied is proposed to solve elliptic unilateral problems. The switching algorithm is firstly presented by J. M. Aitchison for the Signorini Problems of Laplace operator. We extends it to the elliptic operator and get the new algorithm based on the BEM. The detail of the algorithm, and the program codes are given. The advantage of the new algorithm is that it is easy to be implemented effectively and quickly. It only needs a little modification of the BEM programming. The numerical tests show that the new algorithm is effective and conventional.