Abstract
We present a two-grid finite element scheme for the approximation of a second-order nonlinear hyperbolic equation in two space dimensions. In the two-grid scheme, the full nonlinear problem is solved only on a coarse grid of sizeH. The nonlinearities are expanded about the coarse grid solution on the fine gird of sizeh. The resulting linear system is solved on the fine grid. Some a priori error estimates are derived with theH1-normO(h+H2)for the two-grid finite element method. Compared with the standard finite element method, the two-grid method achieves asymptotically same order as long as the mesh sizes satisfyh=O(H2).
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