Abstract
A new family of hybrid discontinuous Galerkin methods is studied for second-order elliptic equations. Our proposed method is a generalization of the cell boundary element (CBE) method [Y. Jeon and E.-J. Park, Appl. Numer. Math., 58 (2008), pp. 800-814], which allows high order polynomial approximations. Our method can be viewed as a hybridizable discontinuous Galerkin method [B. Cockburn, J. Gopalakrishnan, and R. Lazarov, SIAM J. Numer. Anal., 47 (2009), pp. 1319-1365] using a Bauman-Oden-type local solver. The method conserves the mass in each element and the average flux is continuous across the interelement boundary for even-degree polynomial approximations. Optimal order error estimates measured in the energy norm are proved. Numerical examples are presented to show the performance of the method.
| Original language | English |
|---|---|
| Pages (from-to) | 1968-1983 |
| Number of pages | 16 |
| Journal | SIAM Journal on Numerical Analysis |
| Volume | 48 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - 2010 Dec 15 |
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All Science Journal Classification (ASJC) codes
- Numerical Analysis
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A hybrid discontinuous galerkin method for elliptic problems. / Jeon, Youngmok; Park, Eun-Jae.
In: SIAM Journal on Numerical Analysis, Vol. 48, No. 5, 15.12.2010, p. 1968-1983.Research output: Contribution to journal › Article
TY - JOUR
T1 - A hybrid discontinuous galerkin method for elliptic problems
AU - Jeon, Youngmok
AU - Park, Eun-Jae
PY - 2010/12/15
Y1 - 2010/12/15
N2 - A new family of hybrid discontinuous Galerkin methods is studied for second-order elliptic equations. Our proposed method is a generalization of the cell boundary element (CBE) method [Y. Jeon and E.-J. Park, Appl. Numer. Math., 58 (2008), pp. 800-814], which allows high order polynomial approximations. Our method can be viewed as a hybridizable discontinuous Galerkin method [B. Cockburn, J. Gopalakrishnan, and R. Lazarov, SIAM J. Numer. Anal., 47 (2009), pp. 1319-1365] using a Bauman-Oden-type local solver. The method conserves the mass in each element and the average flux is continuous across the interelement boundary for even-degree polynomial approximations. Optimal order error estimates measured in the energy norm are proved. Numerical examples are presented to show the performance of the method.
AB - A new family of hybrid discontinuous Galerkin methods is studied for second-order elliptic equations. Our proposed method is a generalization of the cell boundary element (CBE) method [Y. Jeon and E.-J. Park, Appl. Numer. Math., 58 (2008), pp. 800-814], which allows high order polynomial approximations. Our method can be viewed as a hybridizable discontinuous Galerkin method [B. Cockburn, J. Gopalakrishnan, and R. Lazarov, SIAM J. Numer. Anal., 47 (2009), pp. 1319-1365] using a Bauman-Oden-type local solver. The method conserves the mass in each element and the average flux is continuous across the interelement boundary for even-degree polynomial approximations. Optimal order error estimates measured in the energy norm are proved. Numerical examples are presented to show the performance of the method.
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UR - http://www.scopus.com/inward/citedby.url?scp=78649911138&partnerID=8YFLogxK
U2 - 10.1137/090755102
DO - 10.1137/090755102
M3 - Article
AN - SCOPUS:78649911138
VL - 48
SP - 1968
EP - 1983
JO - SIAM Journal on Numerical Analysis
JF - SIAM Journal on Numerical Analysis
SN - 0036-1429
IS - 5
ER -