An optimal projection method for bilateral obstacle problems

We propose a projection method for bilateral obstacle problems, with an optimal choice of a key parameter. The problem is discretized into a double obstacle form using finite differences, and is reformulated equivalently as a projection-based fixed point problem. A projection iterative method is then employed for numerical solution, and a successive over-relaxation (SOR)-type projection method with an optimal parameter is developed to enhance performance. Convergence results are presented with matrix analysis, and the optimal parameter and relaxation factor are estimated by extreme eigenvalues of the iterative matrix and the balance principle respectively. Numerical experiments validate the theoretical findings.