| Title:
|
A posteriori upper and lower error bound of the high-order discontinuous Galerkin method for the heat conduction equation (English) |
| Author:
|
Šebestová, Ivana |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
59 |
| Issue:
|
2 |
| Year:
|
2014 |
| Pages:
|
121-144 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
discontinuous Galerkin method |
| Keyword:
|
Helmholtz decomposition |
| Keyword:
|
averaging interpolation operator |
| Keyword:
|
Euler backward scheme |
| Keyword:
|
residual-based a posteriori error estimate |
| Keyword:
|
local cut-off function |
| MSC:
|
65M15 |
| MSC:
|
65M60 |
| idZBL:
|
Zbl 06362217 |
| idMR:
|
MR3183468 |
| DOI:
|
10.1007/s10492-014-0045-7 |
| . |
| Date available:
|
2014-03-20T08:16:51Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143624 |
| . |
| Reference:
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| Reference:
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