Explicit error bounds for nonconforming approximation of the heat equation

Abstract

In this paper we present an efficient computable error bounds for nonconforming finite element discretization of the heat equation. For this discretization, we present a posteriori error estimates based on explicit potential and equilibrated flux reconstructions. The indicators provide error upper bounds that are global in space and in time, and error lower bounds that are global in space and local in time. Numerical experiments illustrate the theoretical performance of the error estimator through two examples, where the mesh refinement and coarsening occur in the correct regions and the obtained meshes follow the singularity of
the solution.