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A residual-based error formula for a class of transport equations

Published online by Cambridge University Press:  09 May 2003

M. JUNK ,
A. UNTERREITER  and
F. ZINGSHEIM
M. JUNK
Affiliation:
Universität Kaiserslautern, D-67663 Kaiserslautern, Germany email: junk@mathematik.uni-kl.de
A. UNTERREITER
Affiliation:
TU Berlin, Institut für Mathematik, MA 6-3, 10623 Berlin, Germany email: unterreiter@math.tu-berlin.de
F. ZINGSHEIM
Affiliation:
LMS Deutschland GmbH, Luxemburger Strasse 7, D-67657 Kaiserslautern, Germany email: Frank.Zingsheim@lms-ge.de
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Abstract

We present an exact residual based error formula in natural norms for a class of transport equations. The derivation of the error formula relies on an abstract formulation in a general Hilbert space setting. The key role is played by the validity of an inversion formula. Its verification is for particular radiative transfer equations equivalent to the identification of strong and weak traces. The residual based error formula can be used in the design of efficient and accurate simulations of the cooling process of high quality glass [5].

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 14 , Issue 2 , April 2003 , pp. 181 - 200
Copyright
2003 Cambridge University Press

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