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

Karakashian, Ohannes; Makridakis, Charalambos

doi:10.1090/S0025-5718-04-01654-0

Convergence of a continuous Galerkin method with mesh modification for nonlinear wave equations
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by Ohannes Karakashian and Charalambos Makridakis;

Math. Comp. 74 (2005), 85-102

DOI: https://doi.org/10.1090/S0025-5718-04-01654-0

Published electronically: April 20, 2004

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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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