Abstract
An unconditionally stable fully discrete finite element method for the Korteweg-de Vries equation is presented. In addition to satisfying optimal order global estimates, it is shown that this method is superconvergent at the nodes. The algorithm is derived from the conservative method proposed by the second author by the introduction of a small time-independent forcing term into the discrete equations. This term is a form of the quasiprojection which was first employed in the analysis of superconvergence phenomena for parabolic problems. However, in the present work, unlike in the parabolic case, the quasiprojection is used as perturbation of the discrete equations and does not affect the choice of initial values.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 23-36 |
| Number of pages | 14 |
| Journal | Mathematics of Computation |
| Volume | 38 |
| Issue number | 157 |
| DOIs | |
| State | Published - Jan 1 1982 |
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A superconvergent finite element method for the korteweg-de vries equation. / Arnold, Douglas N.; Winther, Ragnar.
In: Mathematics of Computation, Vol. 38, No. 157, 01.01.1982, p. 23-36.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A superconvergent finite element method for the korteweg-de vries equation
AU - Arnold, Douglas N.
AU - Winther, Ragnar
PY - 1982/1/1
Y1 - 1982/1/1
N2 - An unconditionally stable fully discrete finite element method for the Korteweg-de Vries equation is presented. In addition to satisfying optimal order global estimates, it is shown that this method is superconvergent at the nodes. The algorithm is derived from the conservative method proposed by the second author by the introduction of a small time-independent forcing term into the discrete equations. This term is a form of the quasiprojection which was first employed in the analysis of superconvergence phenomena for parabolic problems. However, in the present work, unlike in the parabolic case, the quasiprojection is used as perturbation of the discrete equations and does not affect the choice of initial values.
AB - An unconditionally stable fully discrete finite element method for the Korteweg-de Vries equation is presented. In addition to satisfying optimal order global estimates, it is shown that this method is superconvergent at the nodes. The algorithm is derived from the conservative method proposed by the second author by the introduction of a small time-independent forcing term into the discrete equations. This term is a form of the quasiprojection which was first employed in the analysis of superconvergence phenomena for parabolic problems. However, in the present work, unlike in the parabolic case, the quasiprojection is used as perturbation of the discrete equations and does not affect the choice of initial values.
UR - http://www.scopus.com/inward/record.url?scp=84968517899&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84968517899&partnerID=8YFLogxK
U2 - 10.1090/S0025-5718-1982-0637284-8
DO - 10.1090/S0025-5718-1982-0637284-8
M3 - Article
VL - 38
SP - 23
EP - 36
JO - Mathematics of Computation
JF - Mathematics of Computation
SN - 0025-5718
IS - 157
ER -