The arbitrary order mixed mimetic finite difference method for the diffusion equation (Q2814661)

The authors present a new family of mimetic finite difference schemes that extends to arbitrary order of accuracy of the approximation of the scalar unknown and the flux developed by \textit{F. Brezzi} et al. [SIAM J. Numer. Anal. 43, No. 5, 1872--1896 (2005; Zbl 1108.65102)]. The well-posedness of the method and the convergence of the approximation are proved theoretically and convergence estimates for both the scalar and the flux variable are derived. The behavior of the method in solving diffusion problems with variable diffusion tensor is investigated experimentally and the numerical results confirm the convergence rates that are expected from the theory. An ultraconvergence effect is visible for the scalar variable when the error is measured in the mesh-dependent norm induced by the mimetic inner product for scalar functions.