FE-HMM For Nonlinear Elliptic Problems With Highly Oscillatory Coefficients

In this thesis,we propose a new method for nonlinear elliptic problems with highly oscillatory coefficients.Firstly,we introduce the finite element method(FEM)and its error estimates.Numerical results implemented in matlab confirm the accuracy of FEM.Secondly,we introduce the heterogeneous multiscale method(HMM).Its error estimates are verified by several numerical examples.Finally,we introduce the fixed-point iteration in the framework of FE-HMM to solve nonlinear elliptic problems with highly oscillatory coefficients.Numerical results show that the new method has the same accuracy as that in the linear case.