Meshless numerical analysis of partial differential equations with nonlinear inequality constraints

A meshless method for the numerical solution of partial differential equations with nonlinear inequality constraints is discussed in this paper. The original nonlinear inequality problem is linearized as a sequence of linear equality problems, and then discrete linear system of algebraic equations is formed. This meshless method only requires nodes on the boundary of the domain, and it does not require any numerical integrations. Numerical experiments indicate that this method is very effective for nonlinear inequality problems and has good convergence rate and high computational efficiency.