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

作者：Sebestova Ivana^*

来源：Applications of Mathematics, 2014, 59(2): 121-144.

DOI：10.1007/s10492-014-0045-7

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.

• 出版日期2014-4