Abstract

Error estimates are proved for finite-element approximations to the solution of an initial boundary value problem for nonlinear second-order hyperbolic partial differential equations. Optimal order rates of convergence in L 2 are shown for single-step fully discrete schemes which are linearized by extrapolations. The order of accuracy ν in time is 2, 3 or 4. A class of iterative methods for approximately solving the fully discrete equations is analyzed and optimal order rates of convergence are also obtained.

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