Localized solutions and filtering mechanisms for the discontinuous Galerkin semi-discretizations of the 1-d wave equation
Marica A, Zuazua E (2010)
Publication Type: Journal article
Publication year: 2010
Journal
Book Volume: 348
Pages Range: 1087-1092
Journal Issue: 19-20
DOI: 10.1016/j.crma.2010.09.012
Abstract
We perform a complete Fourier analysis of the semi-discrete 1 - d wave equation obtained through a P-1 discontinuous Galerkin (DG) approximation of the continuous wave equation on an uniform grid The resulting system exhibits the interaction of two types of components a physical one and a spurious one related to the possible discontinuities that the numerical solution allows Each dispersion relation contains critical points where the corresponding group velocity vanishes Following previous constructions we rigorously build wave packets with arbitrarily small velocity of propagation concentrated either on the physical or on the spurious component We also develop filtering mechanisms aimed at recovering the uniform velocity of propagation of the continuous solutions Finally some applications to numerical approximation issues of control problems are also presented (C) 2010 Published by Elsevier Masson SAS on behalf of Academie des sciences
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APA:
Marica, A., & Zuazua, E. (2010). Localized solutions and filtering mechanisms for the discontinuous Galerkin semi-discretizations of the 1-d wave equation. Comptes Rendus Mathematique, 348(19-20), 1087-1092. https://doi.org/10.1016/j.crma.2010.09.012
MLA:
Marica, Aurora, and Enrique Zuazua. "Localized solutions and filtering mechanisms for the discontinuous Galerkin semi-discretizations of the 1-d wave equation." Comptes Rendus Mathematique 348.19-20 (2010): 1087-1092.
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