Mimetic finite differences for nonlinear and control problems
Saturday 9th March 2013
Antonietti, P.F.; Beirao da Veiga, L.; Bigoni, N.; Verani, M.
In this paper we review some recent applications of the mimetic finite difference method to nonlinear problems (variational inequalities and quasilinear elliptic equations) and optimal control problems governed by linear elliptic partial differential equations. Several numerical examples show the effectiveness of mimetic finite differences in building accurate and robust numerical approximations. Finally, we draw some conclusions highlighting possible further applications of the mimetic finite difference method to nonlinear Stokes equations and shape optimization problems.