Monotone enclosure for nonlinear PDEs using multigrid techniques (Q1184808)

The author investigates two possibilities to include numerical solutions of weakly nonlinear elliptic boundary value problems. For the case of a single equation an algorithm combining the including properties of nonlinear monotone-including iteration processes with the efficiency of FAS is proposed. The second way of solving nonlinear differential equations consists in the following steps: linearize the given equations by a conventional monotone-including method and solve the resulting linear equations by a linear multigrid method. It is demonstrated that this way is very convenient if a weakly coupled system of equations is given. The efficiency of the proposed algorithms is illustrated by numerical examples.