On the Mathematical Analysis and Numerical Approximation of a System of Nonlinear Parabolic PDEs
Copyright policy )On the Mathematical Analysis and Numerical Approximation of a System of Nonlinear Parabolic PDEs
In this paper we consider a boundary value problem for a system of 2 nonlinear parabolic PDEs e.g. arising in the context of flow and transport in porous media. The flow model is based on tho nonlinear Richard’s equation problem and is combined with the transport equation through saturation and Darcy’s velocity (discharge) terms. The convective terms are approximated by means of the method of characteristics initiated by P. Pironneau [Num. Math. 38 (1982), 871–885] and R. Douglas and T. F. Russel [SIAM J. Num. Anal. 19 (1982), 309–332]. The nonlinear terms in Richard’s equation are approximated by means of a relaxation scheme applied by W. Jäger and J. Kačur [RAIRO Model. Math. Anal. Num. 29 (1995), 605–627] and J. Kačur [IMA J. Num. Anal. 19 (1999), 119–154; SIAM J. Num. Anal. 39 (1999), c 290–316]. The convergence of the approximation method is proved.
- Comenius University Slovakia
- Ghent University Belgium
Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs, relaxation method, Nonlinear parabolic equations, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Initial-boundary value problems for second-order parabolic systems, convection-diffusion with adsorption, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, method of characteristics, contaminant transport
Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs, relaxation method, Nonlinear parabolic equations, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Initial-boundary value problems for second-order parabolic systems, convection-diffusion with adsorption, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, method of characteristics, contaminant transport
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