A Two-Grid Finite Element Method for a Second-Order Nonlinear Hyperbolic Equation

الملخص EN

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 size H.

The nonlinearities are expanded about the coarse grid solution on the fine gird of size h.

The resulting linear system is solved on the fine grid.

Some a priori error estimates are derived with the H1-norm O(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 satisfy h=O(H2).