Numerical analysis and computation of a multi-order laminated microstructure

The mesh transformation method is applied in a finite element approximation to a multi-well problem. It is proved that, compared with standard finite element methods, significantly higher convergence rate for the finite element approximations of multi-level microstructures can be obtained by combining the mesh transformation method with the periodic relaxation technique. Numerical examples are given to show the method can be efficiently implemented in computing multi-level microstructures.