A 2-LEVEL NEWTON, FINITE-ELEMENT ALGORITHM FOR APPROXIMATING ELECTRICALLY CONDUCTING INCOMPRESSIBLE FLUID-FLOWS

We consider the approximation of stationary, electrically conducting, incompressible fluid flow problems at small magnetic Reynolds number. The finite element discretization of these systems leads to a very lar ge system of nonlinear equations. We consider a solution algorithm whi ch involves solving a much smaller number of nonlinear equations on a coarse mesh, then one large linear system on a fine mesh. Under a uniq ueness condition, this one-step, two-level Newton-FEM procedure is sho wn to produce an optimally accurate solution. This result extends both the two-level method of Xu [1,2] from elliptic boundary value problem s to MHD problems, and the energy norm error analysis of Peterson [3] (see also [4]) of MHD problems at a small magnetic Reynolds number to L2 error estimates and multilevel discretization and solution procedur es.