Mimetic finite difference approximation of quasilinear elliptic problems

In this work we approximate the solution of a quasilinear elliptic problem of monotone type by using the Mimetic Finite Difference (MFD) method. Under a suitable approximation assumption, we prove that the MFD approximate solution converges, with optimal rate, to the exact solution in a mesh-dependent energy norm. The resulting nonlinear discrete problem is then solved iteratively via linearization by applying the Kačanov method. The convergence of the Kačanov algorithm in the discrete mimetic framework is also proved. Several numerical experiments confirm the theoretical analysis.