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 H and a linear system on a fine grid space with mesh size h. It follows from error estimates that asymptotically optimal accuracy can be obtained as long as the mesh sizes satisfy H = O(h(1/2)) in the L-2 norm. Some numerical examples are presented to illustrate the theoretical results. (C) 2013 Elsevier Ltd. All rights reserved.
expanded mixed finite element two-grid method nonlinear elliptic problem