A Unified Framework for a posteriori Error Estimation in Elliptic and Parabolic Problems with Application to Finite Volumes

We present a unified framework based on potential and flux reconstruction for guaranteed and efficient a posteriori error estimation. We consider as model problems the Laplace equation, the singularly perturbed convection-diffusion-reaction equation, and the heat equation. The analysis is performed for a wide class of space discretization schemes. Three simple conditions need to be verified, which we do for cell- and vertex-centered finite volumes for all model problems.