Abstract
A weighted-norm first-order system least-squares (FOSLS) method for div/curl problems with edge singularities is presented. Traditional finite element methods, including least-squares methods, often suffer from a global loss of accuracy due to the influence of a nonsmooth solution near polyhedral edges. By minimizing a modified least-squares functional, optimal accuracy in weighted and nonweighted norms is recovered. Error estimates with and without mesh refinements are presented, and numerical results are given to confirm the theory.
| Original language | English |
|---|---|
| Pages (from-to) | 1619-1639 |
| Number of pages | 21 |
| Journal | SIAM Journal on Numerical Analysis |
| Volume | 46 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2008 Nov 10 |
Fingerprint
All Science Journal Classification (ASJC) codes
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics
Cite this
}
Weighted-norm first-order system least-squares (FOSLS) for div/curl systems with three dimensional edge singularities. / Lee, E.; Manteuffel, T. A.; Westphal, C. R.
In: SIAM Journal on Numerical Analysis, Vol. 46, No. 3, 10.11.2008, p. 1619-1639.Research output: Contribution to journal › Article
TY - JOUR
T1 - Weighted-norm first-order system least-squares (FOSLS) for div/curl systems with three dimensional edge singularities
AU - Lee, E.
AU - Manteuffel, T. A.
AU - Westphal, C. R.
PY - 2008/11/10
Y1 - 2008/11/10
N2 - A weighted-norm first-order system least-squares (FOSLS) method for div/curl problems with edge singularities is presented. Traditional finite element methods, including least-squares methods, often suffer from a global loss of accuracy due to the influence of a nonsmooth solution near polyhedral edges. By minimizing a modified least-squares functional, optimal accuracy in weighted and nonweighted norms is recovered. Error estimates with and without mesh refinements are presented, and numerical results are given to confirm the theory.
AB - A weighted-norm first-order system least-squares (FOSLS) method for div/curl problems with edge singularities is presented. Traditional finite element methods, including least-squares methods, often suffer from a global loss of accuracy due to the influence of a nonsmooth solution near polyhedral edges. By minimizing a modified least-squares functional, optimal accuracy in weighted and nonweighted norms is recovered. Error estimates with and without mesh refinements are presented, and numerical results are given to confirm the theory.
UR - http://www.scopus.com/inward/record.url?scp=55349109992&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=55349109992&partnerID=8YFLogxK
U2 - 10.1137/06067345X
DO - 10.1137/06067345X
M3 - Article
AN - SCOPUS:55349109992
VL - 46
SP - 1619
EP - 1639
JO - SIAM Journal on Numerical Analysis
JF - SIAM Journal on Numerical Analysis
SN - 0036-1429
IS - 3
ER -