Nowadays a variety of numerical methods are being used for solution of engineering problems. A new emerging category of methods are those requiring no mesh of elements in solution process. One of the recently developed versions of the so called “meshless” methods is based on using collocation approach in satisfaction of the governing differential equation and boundary conditions. The method is sometime called as Finite Point Method(FPM). Similar to other numerical methods approximation plays an important role in the solution procedure and since the method is rather new, the problem of error evaluation is still an open discussion. In this study attempts are made to ddevise a reliable error estimator/indicator procedure for FPM method. Both recovery and residual based error estimation approaches are based in this study. In the context of recovery based error estimation a new version of averaging of the gradients based on using Gaussian weight functions as well as some other recovery approaches for displacements and the gradients considering equilibrium equations as side conditions, are developed and discussed. It has been shown that such recovered fields suffer from lack of superconvergence but considering equilibrium equations as side conditions slightly improves the rates of convergence. In the context of residual based error estimation instead of using residual, which vanishes at nodes, a norm of its gradients is considered as an indicator of the error. It has been shown that gradients of residual can predict the error in Hessian of the stresses. Several heat and elasticity (plane stress) problems are solved to show the performance of such an error indicator. The results show excellent agreement between the indicator and the true error.
