| Title:
|
Optimal convergence and a posteriori error analysis of the original DG method for advection-reaction equations (English) |
| Author:
|
Zhang, Tie |
| Author:
|
Zhang, Shuhua |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
60 |
| Issue:
|
1 |
| Year:
|
2015 |
| Pages:
|
1-20 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider the original DG method for solving the advection-reaction equations with arbitrary velocity in $d$ space dimensions. For triangulations satisfying the flow condition, we first prove that the optimal convergence rate is of order $k+1$ in the $L_2$-norm if the method uses polynomials of order $k$. Then, a very simple derivative recovery formula is given to produce an approximation to the derivative in the flow direction which superconverges with order $k+1$. Further we consider a residual-based a posteriori error estimate and give the global upper bound and local lower bound on the error in the DG-norm, which is stronger than the $L_2$-norm. The key elements in our a posteriori analysis are the saturation assumption and an interpolation estimate between the DG spaces. We show that the a posteriori error bounds are efficient and reliable. Finally, some numerical experiments are presented to illustrate the theoretical analysis. (English) |
| Keyword:
|
discontinuous Galerkin method |
| Keyword:
|
advection-reaction equation |
| Keyword:
|
optimal convergence rate |
| Keyword:
|
a posteriori error estimate |
| MSC:
|
65M60 |
| MSC:
|
65N15 |
| MSC:
|
65N30 |
| idZBL:
|
Zbl 06391459 |
| idMR:
|
MR3299870 |
| DOI:
|
10.1007/s10492-015-0082-x |
| . |
| Date available:
|
2015-01-09T13:52:20Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144089 |
| . |
| Reference:
|
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