Search

In this paper, two-grid methods for characteristic finite volume element solutions are presented for the semi-linear Sobolev equation. The method is based on the methods of characteristics, two-grid method and the finite volume element method. The nonsymmetric and nonlinear iterations are only executed on the coarse grid (with grid size H). And the fine-grid solution (with grid size h) can be obtained by a single symmetric and linear step. It is proved that the coarse grid can be much coarser than the fine grid. The two-grid methods achieve asymptotically optimal approximation as long as the mesh sizes satisfy h = O(H³). As a result, solving such a large semi-linear Sobolev equations will not be much more difficult than solving one single linearized equation. [ABSTRACT FROM AUTHOR]