# A posteriori error analysis for parabolic variational inequalities

Kyoung-Sook Moon; Ricardo H. Nochetto; Tobias von Petersdorff; Chen-song Zhang

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

- Volume: 41, Issue: 3, page 485-511
- ISSN: 0764-583X

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topMoon, Kyoung-Sook, et al. "A posteriori error analysis for parabolic variational inequalities." ESAIM: Mathematical Modelling and Numerical Analysis 41.3 (2007): 485-511. <http://eudml.org/doc/250072>.

@article{Moon2007,

abstract = {
Motivated by the pricing of American options for baskets we
consider a parabolic variational inequality in a bounded
polyhedral domain $\Omega\subset\mathbb\{R\}^d$ with a continuous piecewise
smooth obstacle. We formulate a fully discrete method by using
piecewise linear finite elements in space and the backward Euler
method in time. We define an a posteriori error estimator and show
that it gives an upper bound for the error in
L2(0,T;H1(Ω)). The error estimator is localized in the
sense that the size of the elliptic residual is only relevant in
the approximate non-contact region, and the approximability of the
obstacle is only relevant in the approximate contact region. We
also obtain lower bound results for the space error indicators in
the non-contact region, and for the time error estimator.
Numerical results for d=1,2 show that the error estimator decays
with the same rate as the actual error when the space meshsize h
and the time step τ tend to zero. Also, the error indicators
capture the correct behavior of the errors in both the contact and
the non-contact regions.
},

author = {Moon, Kyoung-Sook, Nochetto, Ricardo H., von Petersdorff, Tobias, Zhang, Chen-song},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {A posteriori error analysis; finite element method;
variational inequality; American option pricing.; backward Euler method; numerical results; a posteriori error analysis; variational inequality; American option pricing},

language = {eng},

month = {8},

number = {3},

pages = {485-511},

publisher = {EDP Sciences},

title = {A posteriori error analysis for parabolic variational inequalities},

url = {http://eudml.org/doc/250072},

volume = {41},

year = {2007},

}

TY - JOUR

AU - Moon, Kyoung-Sook

AU - Nochetto, Ricardo H.

AU - von Petersdorff, Tobias

AU - Zhang, Chen-song

TI - A posteriori error analysis for parabolic variational inequalities

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2007/8//

PB - EDP Sciences

VL - 41

IS - 3

SP - 485

EP - 511

AB -
Motivated by the pricing of American options for baskets we
consider a parabolic variational inequality in a bounded
polyhedral domain $\Omega\subset\mathbb{R}^d$ with a continuous piecewise
smooth obstacle. We formulate a fully discrete method by using
piecewise linear finite elements in space and the backward Euler
method in time. We define an a posteriori error estimator and show
that it gives an upper bound for the error in
L2(0,T;H1(Ω)). The error estimator is localized in the
sense that the size of the elliptic residual is only relevant in
the approximate non-contact region, and the approximability of the
obstacle is only relevant in the approximate contact region. We
also obtain lower bound results for the space error indicators in
the non-contact region, and for the time error estimator.
Numerical results for d=1,2 show that the error estimator decays
with the same rate as the actual error when the space meshsize h
and the time step τ tend to zero. Also, the error indicators
capture the correct behavior of the errors in both the contact and
the non-contact regions.

LA - eng

KW - A posteriori error analysis; finite element method;
variational inequality; American option pricing.; backward Euler method; numerical results; a posteriori error analysis; variational inequality; American option pricing

UR - http://eudml.org/doc/250072

ER -

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