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A preconditioned iterative solution scheme for nonlinear parabolic systems arising in air pollution modeling. (English) Zbl 1291.65267

Summary: A preconditioned iterative solution method is presented for nonlinear parabolic transport systems. The ingredients are implicit Euler discretization in time and finite element discretization in space, then an outer-inner (outer damped inexact Newton method with inner preconditioned conjugate gradient) iteration, further, as a main part, preconditioning via an \(\ell\)-tuple of independent elliptic operators. Numerical results show that the suggested method works properly for a test problem in air pollution modeling.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
92D40 Ecology
65M22 Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs
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