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Additive and hybrid nonlinear two-level Schwarz methods and energy minimizing coarse spaces for unstructured grids. (English) Zbl 1453.65428

The goal of this article is to discuss nonlinear left-preconditioners based on an overlapping (Schwarz) domain decomposition method in the approximation of nonlinear elliptic equations driven by the \(p\)-Laplace operator. The authors introduce four different additively and multiplicatively coupled two-level methods based on Galerkin projections. These four methods allow the use of various coarse spaces, such as coarse spaces based on energy-minimizing extensions which are easily adaptable to irregular domain decomposition. In particular, coarse multiscale finite element method are considered and it is shown that they outperform classical approaches for certain heterogeneous nonlinear problems.

MSC:

65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65F08 Preconditioners for iterative methods
65F10 Iterative numerical methods for linear systems
65H10 Numerical computation of solutions to systems of equations
65H20 Global methods, including homotopy approaches to the numerical solution of nonlinear equations
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

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