Abstract
Two-grid fully discrete finite element approximations of the solution for a nonlinear hyperbolic integro-differential equation are considered and analyzed in this paper. The H1-norm error estimate is derived, which shows that the optimal convergence order can be obtained when the coarse-grid of size H and the fine-grid of size h satisfy h=O(H2). Besides reducing the storage and saving a large amount of time, two-grid methods also keep the accuracy of convergence in calculations. Numerical examples are given to support our theoretical results and demonstrate the efficiency of the methods.
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