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 | References | Similar Articles | Additional Information

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