Global and uniform convergence of subspace correction methods for some convex optimization problems
Mathematics of Computation
Two-Grid Discontinuous Galerkin Method for Quasi-Linear Elliptic Problems
Journal of Scientific Computing
Computers & Mathematics with Applications
Numerical and computational efficiency of solvers for two-phase problems
Computers & Mathematics with Applications
Hi-index | 0.00 |
We consider a two-level method for the discretization and solution of nonlinear boundary value problems. The method basically involves (i) solving the nonlinear problem on a {\it very} coarse mesh, (ii) linearizing about the coarse mesh solution, and solving the linearized problem on the fine mesh, one time! We analyze the accuracy of this procedure for strongly monotone nonlinear operators (\S2) and general semilinear elliptic boundary value problems (without monotonicity assumptions). In particular, the scaling between the fine and coarse mesh widths required to ensure optimal accuracy of the fine mesh solution is derived as a byproduct of the error estimates herein.