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

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**74**(2005), 85-102 Request permission

## 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.## References

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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
- MR Author ID: 289627
- Email: makr@tem.uoc.gr
- Received by editor(s): November 20, 2001
- Received by editor(s) in revised form: May 7, 2003
- Published electronically: April 20, 2004
- © Copyright 2004 American Mathematical Society
- Journal: Math. Comp.
**74**(2005), 85-102 - MSC (2000): Primary 65M60, 65M12
- DOI: https://doi.org/10.1090/S0025-5718-04-01654-0
- MathSciNet review: 2085403