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.

Notes on the convergence order of gradient schemes for time fractional differential equations

“…It has been developed recently in [5] and it includes, for instance, conforming and nonconforming finite element, mixed finite element, hybrid mixed mimetic family, some Multi-Point Flux approximation finite volume schemes, and some discontinuous Galerkin schemes. It has been applied successfully to approximate numerous models, see for instance [4,6,7] and references therein. The above model is known to describe well the anomalous diffusion phenomena in highly heterogeneous aquifers and complex viscoelastic materials, see [9].…”