Gradient schemes: a generic framework for the discretisation of linear, nonlinear and nonlocal elliptic and parabolic equations (Q2857739)

The paper is interested in the approximation of the boundary value problem for general nonlinear elliptic equations and also of the initial value problem for a nonlinear parabolic problem. Gradient schemes are considered and the convergence is proven provided that the properties, namely coercivity, consistency, limit-conformity and compactness, are satisfied. Furthermore, it is shown that the schemes of the hybrid mimetic mixed family may be seen as gradient schemes meeting these four properties. Therefore, the convergence is proven for the above-mentioned problems and the mimetic finite difference schemes.