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Monotone enclosure for nonlinear PDEs using multigrid techniques. (English) Zbl 0747.65091
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.
Reviewer: M.Jung (Chemnitz)

MSC:
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65H10 Numerical computation of solutions to systems of equations
35J65 Nonlinear boundary value problems for linear elliptic equations
Software:
MGOO
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