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Keywords:
discontinuous Galerkin method; Helmholtz decomposition; averaging interpolation operator; Euler backward scheme; residual-based a posteriori error estimate; local cut-off function
discontinuous Galerkin method; Helmholtz decomposition; averaging interpolation operator; Euler backward scheme; residual-based a posteriori error estimate; local cut-off function
Summary:
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.
References:
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