The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (261 KB) | Abstract as PDF | Metadata | Table of Contents | ZAA summary
Volume 28, Issue 3, 2009, pp. 305–332
DOI: 10.4171/ZAA/1387

Published online: 2009-09-30

On the Mathematical Analysis and Numerical Approximation of a System of Nonlinear Parabolic PDEs

J. Kačur[1], B. Malengier[2] and R. Van Keer[3]

(1) Comenius University, Bratislava, Slovak Republic
(2) Universiteit Gent, Belgium
(3) Universiteit Gent, Belgium

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.

Keywords: Relaxation method, method of characteristics, contaminant transport, convection-diffusion with adsorption

Kačur J., Malengier B., Van Keer R.: On the Mathematical Analysis and Numerical Approximation of a System of Nonlinear Parabolic PDEs. Z. Anal. Anwend. 28 (2009), 305-332. doi: 10.4171/ZAA/1387