Kriging-based Finite Element Method: Element-by-element Kriging Interpolation

An enhancement of the finite element method with Kriging shape functions (K-FEM) was recently proposed. In this method, the field variables of a boundary value problem are approximated using element-by-element piecewise Kriging interpolation (el-KI). For each element, the interpolation function is constructed from a set of nodes within a prescribed domain of influence comprising the element and its several layers of neighbouring elements. This paper presents a numerical study on the accuracy and convergence of the el-KI in function fitting problems. Several examples of functions in two-dimensional space are employed in this study. The results show that very accurate function fittings and excellent convergence can be attained by the el-KI.