Multiscale modeling using goal-oriented adaptivity and numerical homogenization. Part I: Mathematical formulation and numerical results

► We formulate a new numerical homogenization method for heterogeneous media. ► The method is tested on a discrete polymer elasticity model. ► One and two dimensional analytical examples are used to verify the method. ► The method is integrated with finite element method. ► We show numerical examples for mesh adaptivity and nonlinear simulations.