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Šebestová, Ivana

A posteriori upper and lower error bound of the high-order discontinuous Galerkin method for the heat conduction equation. (English) Zbl 1324.65119

Appl. Math., Praha 59, No. 2, 121-144 (2014).
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.

Cited in 1 Document

MSC:

65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs

Keywords:

discontinuous Galerkin method; Helmholtz decomposition; averaging interpolation operator; Euler backward scheme; residual-based a posteriori error estimate; local cut-off function; nonstationary heat conduction equation; numerical experiments
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References:

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