Mathematical aspects and computational considerations in the theory of homogenization
Richard C. Morgan · 1982
Elliptic partial differential equations on the infinite domain, which have periodic coefficients, are studied with a view towards formulating numerical methods of approximating the solution. The central result is that the solution admits an integral representation in which one factor of the integrand is the solution of a family of elliptic differential equations, called cell problems, for which the domain of each is based on one period of the coefficients of the original differential equation. Methods of approximating and properties of the solution to the original problem are then derived from similar considerations of the solutions to the cell problems. One method of approximating the solutions to the cell problems corresponds to the mathematically standard homogenization procedure.