Calculation of error over the problem domain is one of the most important concerns in numerical methods. Many researchers have tried to propose a posteriori error estimators or indicators to control the errors and the results. In this dissertation, a probabilistic model is presented which can estimate the distribution of variance of absolute error and contains spatial structure of nodes. This model is used as an error indicator. Then a refinement strategy is developed based on the proposed error indicator. According to the proposed refinement strategy, the refinement can be performed many times based on the user defined percentage of error. The proposed refinement is a type of H-refinement.Then, according to probabilistic concepts, the covariance can present the correlation of nodes locations by considering the spatial structure of nodes. This property of covariance is used for error indicating and formulation of the proposed error indicator. The validation procedure is performed by two types of examples, firstly using mathematical random functions and secondly using an infinite plate with a circular hole. According to the results, themain advantage of this error indicator is definition of a specific formulation for assessment of local changes of the variance of the absolute error field which improves the evaluation of the error field. For the refinement of the problem domain, a refinement strategy is developed and some new nodes are added at the location with maximums error. The number of the additional nodes is based the percentage of error which is defined by the user. In this dissertation, this percentage of error is defined based on the proposed error indicator. Refinement of the problem domain is done until the error values become lesser than the desired values. The spatial structure of nodes is updated in each refinement stage but the parameter remains constant. Therefore refinement can be performed in many stages with one numerical solution of the problem and this reduces the computational costs of the proposed refinement. Results show that boundaries can also be refined using the maximums of the proposed error indicator over the boundaries. Key Words: Error indicator, spatial statistics, Probability, Variance of absolute Error, H-Refinement, EFG