A novel two-grid method for semilinear elliptic equations. (English) Zbl 0795.65077

Xu, Jinchao

SIAM J. Sci. Comput. 15, No. 1, 231-237 (1994).

Author’s summary: A new finite element discretization technique based on two (coarse and fine) subspaces is presented for a semilinear elliptic boundary value problem. The solution of a nonlinear system on the fine space is reduced to the solution of two small (one linear and one nonlinear) systems on the coarse space and a linear system on the fine space. It is shown, both theoretically and numerically, that the coarse space can be extremely coarse and still achieve asymptotically optimal approximation. As a result, the numerical solution of such a nonlinear equation is not signficantly more expensive than the solution of one single linearized equation.

Reviewer: J.D.P.Donnelly (Oxford)

MSC:

65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N55	Multigrid methods; domain decomposition for boundary value problems involving PDEs
35J65	Nonlinear boundary value problems for linear elliptic equations

Keywords:

two-grid method; finite element; semilinear elliptic boundary value problem