Publication Results

Code: 38/2012
Title: Mimetic finite difference approximation of quasilinear elliptic problems
Date: Saturday 15th September 2012
Author(s) : Antonietti, P.f.; Bigoni, N.; Verani, M.
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Abstract: 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 Kacanov method. The convergence of the Kacanov algorithm in the discrete mimetic framework is also proved. Several numerical experiments confirm the theoretical analysis.