Abstract
A new family of locally conservative, finite element methods for a rectangular mesh is introduced to solve second-order elliptic equations. Our approach is composed of generating PDE-adapted local basis and solving a global matrix system arising from a flux continuity equation. Quadratic and cubic elements are analyzed and optimal order error estimates measured in the energy norm are provided for elliptic equations. Next, this approach is exploited to approximate Stokes equations. Numerical results are presented for various examples including the lid driven-cavity problem.
| Original language | English |
|---|---|
| Pages (from-to) | 97-119 |
| Number of pages | 23 |
| Journal | Numerische Mathematik |
| Volume | 123 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2013 Jan 1 |
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All Science Journal Classification (ASJC) codes
- Computational Mathematics
- Applied Mathematics
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New locally conservative finite element methods on a rectangular mesh. / Jeon, Youngmok; Park, Eun-Jae.
In: Numerische Mathematik, Vol. 123, No. 1, 01.01.2013, p. 97-119.Research output: Contribution to journal › Article
TY - JOUR
T1 - New locally conservative finite element methods on a rectangular mesh
AU - Jeon, Youngmok
AU - Park, Eun-Jae
PY - 2013/1/1
Y1 - 2013/1/1
N2 - A new family of locally conservative, finite element methods for a rectangular mesh is introduced to solve second-order elliptic equations. Our approach is composed of generating PDE-adapted local basis and solving a global matrix system arising from a flux continuity equation. Quadratic and cubic elements are analyzed and optimal order error estimates measured in the energy norm are provided for elliptic equations. Next, this approach is exploited to approximate Stokes equations. Numerical results are presented for various examples including the lid driven-cavity problem.
AB - A new family of locally conservative, finite element methods for a rectangular mesh is introduced to solve second-order elliptic equations. Our approach is composed of generating PDE-adapted local basis and solving a global matrix system arising from a flux continuity equation. Quadratic and cubic elements are analyzed and optimal order error estimates measured in the energy norm are provided for elliptic equations. Next, this approach is exploited to approximate Stokes equations. Numerical results are presented for various examples including the lid driven-cavity problem.
UR - http://www.scopus.com/inward/record.url?scp=84871937628&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84871937628&partnerID=8YFLogxK
U2 - 10.1007/s00211-012-0477-5
DO - 10.1007/s00211-012-0477-5
M3 - Article
AN - SCOPUS:84871937628
VL - 123
SP - 97
EP - 119
JO - Numerische Mathematik
JF - Numerische Mathematik
SN - 0029-599X
IS - 1
ER -