A two-grid algorithm for expanded mixed finite element approximations of semi-linear elliptic equations

A semi-linear elliptic problem with variable coefficient is approximated by expanded mixed formulation based on the RTN and BDM mixed finite elements. In order to solve the nonlinear approximation system of equations efficiently, a two-grid algorithm is considered and discussed in this paper. The work includes a small nonlinear system on a coarse grid space with mesh size HH and a linear system on a fine grid space with mesh size hh. It follows from error estimates that asymptotically optimal accuracy can be obtained as long as the mesh sizes satisfy H=O(h1/2)H=O(h1/2) in the L2L2 norm. Some numerical examples are presented to illustrate the theoretical results.