International Science Community Association Research Journal of Engineering Sciences 2278-9472 11 1 2022 01 26 Finite element method for relativistic analysis of wave functions of xenon atom 1 14 EN GOMIS Rama 1 Plasma Physics Laboratory and Interdisciplinary Research, Dakar, Senegal GOMIS Louis 2 Plasma Physics Laboratory and Interdisciplinary Research, Dakar, Senegal DIOUF Yande 3 Group of Solid Physics and Materials Sciences, Dakar, Senegal > Research Paper 2021 8 28 2022 01 26 Taking into account relativistic aspect in quantum calculations, is a fundamental step towards correct modeling of systems involving heavy elements. This modeling involves an appropriate resolution of Schrödinger equation. The present study focuses on Xenon which is a heavy poly electronic atom. This is to calculate on basis of DFT, its radial wave functions for different orbitals, total energies and its effective potential in the ground state. Our motivation through this simulation is to examine the influence of relativistic effects and spin-orbit coupling on these physical grandeur. So, due to the structural complexity of the equation, we carried out the calculations implicitly by the finite element method via a program established from MATLAB software in deterministic mode. The numerical solutions obtained are based on the approximation of the local density (LDA) and that of the generalized gradient (GGA). The results obtained, allowed to describe xenon on a microscopic scale, to understand its structure and to explore the mechanisms that ensure its stability. Finally, our results are in good agreement with theoretical data found in the literature. Copyright@ International Science Community Association