Error Analysis For Finite Element Method Based On Statistical Two-scale Analysis Computing Expected Temperature Filed Of Composites With Random Grains

In this paper, one error estimation of a finite element method based on statistical two-scale analysis (STSA-FEM) for computing the expected temperature field of the composite with random grains was induced. The error estimation of the expected temperature field by the STSA-FEM was obtained.Firstly, based on the properties of the composites with random grains, the probability space for the composites with random grains was introduced. Then, we introduced the expected temperature field and the two-scale temperature field for the composites with random grains. Next, the error estimation of the expected temperature field by the STSA-FEM was analyzed. It was shown that the total error estimation for the expected temperature field by the STSA-FEM was made up of three kinds of errors:the two-scale analysis error, the probability error and the finite element computational error. Finally, the discussion and the numerical example were given to draw some conclusions and some remarks to illustrate how the errors affect the validity of STSA-FEM computing the expected temperature field of the composites with random grains. From the error estimation and the numerical example, the computed homogenization temperature field by STSA-FEM can be alternative to the expected temperature field of the composites with random grains.