3D electromagnetic elastic joint finite element method and stochastic SGILD method

Abstract

In paper [1] in 1975, we proposed 3D elastic problem's Finite Element Method. We used a novel method to construct the high accurate 3D element which has 6 curve surfaces and 20 nodes, independently, which is called isoparametric element in west world. In particular, in 1973, we, in first in the world, discovered a super convergence phenomena of the stress and displacement in Gauss points in the our 20 nodes high accurate element (isoparametric element) [1], i.e., the stress and displacement have o(h4) super convergent rate in Gauss points in the our 3D novel isoparametric element. In this paper, we develop 3D Stochastic SGILD Electromagnetic Elastic Joint Finite Element Method by locally using our 20 nodes high accurate element (isoparametric element) and our stochastic GILD method globally. There are advantages of our new methods for applications in electromagnetic and elastic mechanical engineering. Our new SGILD FEM method overcome the fundamental difficulties in Finite Element Method.