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On monotone and Schwarz alternating methods for nonlinear elliptic PDEs. (English) Zbl 0976.65109

Convergence proofs of some Schwarz alternating methods for nonlinear elliptic problems by the monotone method are given. In particular, an additive Schwarz method for scalar or coupled nonlinear partial differential equations (PDEs) are shown to converge for finitely many subdomains. These methods are applicable to several models in population biology.

MSC:

65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J65 Nonlinear boundary value problems for linear elliptic equations
65N06 Finite difference methods for boundary value problems involving PDEs
92D25 Population dynamics (general)
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References:

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