The finite element method enriched by interpolation covers

► A finite element procedure using interpolation covers is focused upon. ► 3-node 2D and 4-node 3D elements are considered. ► The reliability and efficiency of the procedure are discussed. ► The method is illustrated through the solution of problems. In this paper, we focus on an enriched finite element solution procedure for low-order elements based on the use of interpolation cover functions. We consider the 3-node triangular and 4-node tetrahedral displacement-based elements for two- and three-dimensional analyses, respectively. The standard finite element shape functions are used with interpolation cover functions over patches of elements to increase the convergence of the finite element scheme. The cover functions not only capture higher gradients of a field variable but also smooth out inter-element stress jumps. Since the order of the interpolations in the covers can vary, the method provides flexibility to use different covers for different patches and increases the solution accuracy without any local mesh refinement. As pointed out, the procedure can be derived from various general theoretical approaches and the basic theory has been presented earlier. We evaluate the effectiveness of the method, and illustrate the power of the scheme through the solution of various problems. The method also has potential for the development of error measures.