A posteriori error estimates of the discontinuous Galerkin method for the heat conduction equation

Abstract

The paper deals with a numerical solution of the nonstationary heat equation with mixed Dirichlet/Neumann boundary conditions. The space semi-discretization is carried out with the aid of the interior penalty Galerkin methods and the backward Euler method is employed for the time discretization.

The a posteriori upper error bound is derived.

Keywords

• discontinuous Galerkin method
• a posteriori error estimates
• Helmholtz decomposition