The Use of Finite Elements for Approximation of Field Variables on Local Sub-Domains in a Mesh-Free Way
The paper deals with the numerical implementations of local integral equation formulation for the solution of two-dimensional (2-d) problems in linear elastic media with continuously variable Young’s modulus. Two kinds of the finite element based interpolation are developed for approximation of field variables on local sub-domains around nodal points. One of these approximations can be classified as meshless, since the elements are generated automatically from the predefined nodal points on the analyzed domain. The other one utilizes the predefined mesh of elements. Besides the element based interpolations we present also the meshless Point Interpolation Method. The accuracy, convergence, numerical stability and efficiency of the proposed techniques are tested by numerical examples with using the exact benchmark solutions.
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