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Convergence of a continuous Galerkin method with mesh modification for nonlinear wave equations


Authors: Ohannes Karakashian and Charalambos Makridakis
Journal: Math. Comp. 74 (2005), 85-102
MSC (2000): Primary 65M60, 65M12
DOI: https://doi.org/10.1090/S0025-5718-04-01654-0
Published electronically: April 20, 2004
MathSciNet review: 2085403
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Abstract: We consider space-time continuous Galerkin methods with mesh modification in time for semilinear second order hyperbolic equations. We show a priori estimates in the energy norm without mesh conditions. Under reasonable assumptions on the choice of the spatial mesh in each time step we show optimal order convergence rates. Estimates of the jump in the Riesz projection in two successive time steps are also derived.


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Additional Information

Ohannes Karakashian
Affiliation: Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37966
Email: ohannes@math.utk.edu

Charalambos Makridakis
Affiliation: Department of Applied Mathematics, University of Crete, 714 09 Heraklion, Crete, Greece; IACM-FORTH, 711 10 Heraklion, Crete, Greece
Email: makr@tem.uoc.gr

DOI: https://doi.org/10.1090/S0025-5718-04-01654-0
Received by editor(s): November 20, 2001
Received by editor(s) in revised form: May 7, 2003
Published electronically: April 20, 2004
Article copyright: © Copyright 2004 American Mathematical Society