An error estimate for the approximation of linear parabolic equations by the gradient discretization method

Abstract

We establish an error estimate for fully discrete time-space gradient schemes on a simple linear parabolic equation. This error estimate holds for all the schemes within the framework of the gradient discretisation method: conforming and non conforming finite element, mixed finite element, hybrid mixed mimetic family, some Multi-Point Flux approximation finite volume scheme and some discontinuous Galerkin schemes.