Karátson, János; Kurics, Tamás A preconditioned iterative solution scheme for nonlinear parabolic systems arising in air pollution modeling. (English) Zbl 1291.65267 Math. Model. Anal. 18, No. 5, 641-653 (2013). 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. Cited in 2 Documents 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 Keywords:nonlinear parabolic transport systems; Newton’s method; inner-outer iteration; air pollution models; numerical examples; implicit Euler discretization in time; finite element discretization in space; preconditioning PDFBibTeX XMLCite \textit{J. Karátson} and \textit{T. Kurics}, Math. Model. Anal. 18, No. 5, 641--653 (2013; Zbl 1291.65267) Full Text: DOI