Computation of Discretization Error Using the Rule of Gradient Recovery and Adaptive Refinement of Elements

Since the beginning of modeling physical events by computers, the finite element method has been firmly accepted as one of the most efficient general techniques the numerical solution of a variety of problems encountered in engineering. But no one has provided an answer to accurately determine the discretization error value in analyzing a structural problem using finite element method and there is almost no accessible tool to select suitable sizes for elements and proper types of solutions and the size of each element is selected based on experts’ judgments.
The present paper is an attempt to present a closed-form solution for three-node triangular elements in order to estimate the discretization error in continuous domains by using the rule of gradient recovery and h-refinement adaptivity. Computing the discretization error and diagnosing the suitability of the elements size are possible by the closed-form solution presented.