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 l-tuple of independent elliptic operators. Numerical results show that the suggested method works properly for a test problem in air pollution modeling.
Karatson, J., & Kurics, T. (2013). A preconditioned iterative solution scheme for nonlinear parabolic systems arising in air pollution modeling. Mathematical Modelling and Analysis, 18(5), 641-653. https://doi.org/10.3846/13926292.2013.868841
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