Numerical Homogenization Of Elliptic Equations With Rough Coefficients

Partial Differential Equations with rough coefficients often arise as multiscale problem,which is common in the study of composite material and heterogeneous material.In this thesis,we use traditional Finite Element Method with linear basis,quadratic basis and cubic basis and Gamblet Theory to solve two equations: Scalar Elliptic Equation and Linear Elasticity Equation.After analyzing numerical results,we find that Finite Element Methods can achieve better numerical results using finer mesh and higher order basis functions.Howerver,the higher computational cost using Finite Element Method sometimes is intolerable.Meanwhile,we using Gamblet Theory to solve the equations and find that it is far more efficient that Finite Element Method when solving partial differential equations with rough coefficients.