| Title:
|
On discontinuous Galerkin method and semiregular family of triangulations (English) |
| Author:
|
Prachař, Aleš |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
51 |
| Issue:
|
6 |
| Year:
|
2006 |
| Pages:
|
605-618 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Discretization of second order elliptic partial differential equations by discontinuous Galerkin method often results in numerical schemes with penalties. In this paper we analyze these penalized schemes in the context of quite general triangular meshes satisfying only a semiregularity assumption. A new (modified) penalty term is presented and theoretical properties are proven together with illustrative numerical results. (English) |
| Keyword:
|
discontinuous Galerkin method |
| Keyword:
|
elliptic equations |
| Keyword:
|
penalty method |
| Keyword:
|
semiregular family of triangulations |
| MSC:
|
35J25 |
| MSC:
|
65N12 |
| MSC:
|
65N15 |
| MSC:
|
65N30 |
| idZBL:
|
Zbl 1164.65499 |
| idMR:
|
MR2291785 |
| DOI:
|
10.1007/s10492-006-0024-8 |
| . |
| Date available:
|
2009-09-22T18:27:43Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134656 |
| . |
| Reference:
|
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| Reference:
|
[2] D. N. Arnold: An interior penalty finite element method with discontinuous elements.SIAM J. Numer. Anal. 19 (1982), 742–760. Zbl 0482.65060, MR 0664882, 10.1137/0719052 |
| Reference:
|
[3] D. Arnold, F. Brezzi, B. Cockburn, and D. Marini: Unified analysis of discontinuous Galerkin methods for elliptic problems.SIAM J. Numer. Anal. 39 (2002), 1749–1779. MR 1885715, 10.1137/S0036142901384162 |
| Reference:
|
[4] P. Ciarlet: The Finite Element Method for Elliptic Problems.North Holland, Amsterdam, 1978. Zbl 0383.65058, MR 0520174 |
| Reference:
|
[5] M. Křížek: On semiregular families of triangulations and linear interpolation.Appl. Math. 36 (1991), 223–232. MR 1109126 |
| Reference:
|
[6] B. Rivière, M. F. Wheeler, and V. Girault: Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. Part I.Comput. Geosci. 3 (1999), 337–360. MR 1750076, 10.1023/A:1011591328604 |
| Reference:
|
[7] Ch. Schwab: $p$- and $hp$-Finite Elements Methods.Clarendon Press, Oxford, 1998. MR 1695813 |
| Reference:
|
[8] M. F. Wheeler: An elliptic collocation-finite element method with interior penalties.SIAM J. Numer. Anal. 15 (1978), 152–161. Zbl 0384.65058, MR 0471383, 10.1137/0715010 |
| Reference:
|
[9] V. Jarník: Differential Calculus II.Academia, Prague, 1978. (Czech) |
| . |
