A posteriori upper and lower error bound of the high-order discontinuous Galerkin method for the heat conduction equation

• ID: 2665, RIV: 10283096
• ISSN: 0862-7940, ISBN: not specified
• source: Applications of Mathematics
• keywords: 2nd-order elliptic problems; approximation
• authors: Ivana Šebestová
• authors from KNM: not assigned

Abstract

We deal with the numerical solution of the nonstationary heat conduction equation with mixed Dirichlet/Neumann boundary conditions. The backward Euler method is employed for the time discretization and the interior penalty discontinuous Galerkin method for the space discretization. Assuming shape regularity, local quasi-uniformity, and transition conditions, we derive both a posteriori upper and lower error bounds. The analysis is based on the Helmholtz decomposition, the averaging interpolation operator, and on the use of cut-off functions. Numerical experiments are presented.