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

Jozef Kačur | Zendy; Benny Malengier | Zendy; Roger Van Keer | Zendy

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

Author(s) -

Jozef Kačur,

Benny Malengier,

Roger Van Keer

Publication year - 2009

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/1387

Subject(s) - nonlinear system , mathematics , parabolic partial differential equation , numerical analysis , mathematical analysis , partial differential equation , calculus (dental) , physics , medicine , dentistry , quantum mechanics

In this paper we consider a boundary value problem for a system of 2 nonlinear parabolic PDEs e.g. arising in the context of ow 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. Jager and J. Kacur [RAIRO Model. Math. Anal. Num. 29 (1995), 605-627] and J. Kacur [IMA J. Num. Anal. 19 (1999), 119-154; SIAM J. Num. Anal. 39 (1999), 290-316]. The convergence of the approximation method is proved

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