Abstract and Applied Analysis

Constraint-Preserving Boundary Conditions for the Linearized Baumgarte-Shapiro-Shibata-Nakamura Formulation

Alexander M. Alekseenko

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Abstract

We derive two sets of explicit homogeneous algebraic constraint-preserving boundary conditions for the second-order in time reduction of the linearized Baumgarte-Shapiro-Shibata-Nakamura (BSSN) system. Our second-order reduction involves components of the linearized extrinsic curvature only. An initial-boundary value problem for the original linearized BSSN system is formulated and the existence of the solution is proved using the properties of the reduced system. A treatment is proposed for the full nonlinear BSSN system to construct constraint-preserving boundary conditions without invoking the second order in time reduction. Energy estimates on the principal part of the BSSN system (which is first order in temporal and second order in spatial derivatives) are obtained. Generalizations to the case of nonhomogeneous boundary data are proposed.

Article information

Source
Abstr. Appl. Anal., Volume 2008 (2008), Article ID 742040, 21 pages.

Dates
First available in Project Euclid: 9 September 2008

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1220969171

Digital Object Identifier
doi:10.1155/2008/742040

Mathematical Reviews number (MathSciNet)
MR2407284

Zentralblatt MATH identifier
1148.83305

Citation

Alekseenko, Alexander M. Constraint-Preserving Boundary Conditions for the Linearized Baumgarte-Shapiro-Shibata-Nakamura Formulation. Abstr. Appl. Anal. 2008 (2008), Article ID 742040, 21 pages. doi:10.1155/2008/742040. https://projecteuclid.org/euclid.aaa/1220969171


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