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

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.


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
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