A two-grid method for solving elliptic problems with inhomogeneous boundary conditions

A Galerkin finite element method using a two-grid technique for solving elliptic problems with inhomogeneous essential boundary conditions is considered. At the boundary, the function is approximated by a projection of the given data on a finite dimensional space; in the interior of the domain, a two-grid method is used for solving the algebraic system. An analysis of the L2-error is made and sample computations are provided.