Cover interpolation functions and h-enrichment in finite element method

This paper presents a method to improve the generation of meshes and the accuracy of numerical solutions of elasticity problems, in which two techniques of h-refinement and enrichment are used by interpolation cover functions. Initially, regions which possess desired accuracy are detected. Mesh improvment is done through h-refinement for the elements existing in those regions. Total error of the domain is thus reduced and limited to the allowable range. In order to increase the accuracy of solutions to an excellent level, the results of mesh refinement are reassessed in the next steps and the nodes exceeding the value of allowable error are determined. The method automatically improves the subdomain by increasing the order of interpolation cover functions which yields to solutions of appropriate accuracy. A comparison of solutions achieved by the proposed method with that of other methods and also the accurate solutions for linear elasticity examples proves acceptable efficiency and accuracy of the proposed method. In this research, we illustrate the power of the strategy through the solutions obtained for various problems.