High order FEM for multigrid homogenization

The high order FEM was applied to the multigrid based homogenization and proved to be an efficient method for upscaled solution approximation of problems with rapidly varying, possibly noncontinuous coefficients as well as non coherent (porous) domains that may or may not depict a periodic micro structure and do not have to satisfy the separation condition. Our main contribution is an improved, appropriate for bubble functions, inter-grid mapping. Consequently a fast, exponential convergence of both displacements and stresses was observed in the conducted numerical experiments with respect to the number of degrees of freedom as well as the time of computation. Particularly, the high accuracy of solution derivatives is an important advantage of this homogenization technique that is equivalent to the multiscale FEM.