Solution of double nonlinear problems in porous media by a combined finite volume–finite element algorithm

The combined finite volume–finite element scheme for a double nonlinear parabolic convection-dominated diffusion equation which models the variably saturated flow and contaminant transport problems in porous media is extended. Whereas the convection is approximated by a finite volume method (Multi-P...

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Bibliographic Details
Published in:Applied numerical mathematics 2014-08, Vol.82, p.11-31
Main Authors: Mahmood, Mohammed Shuker, Kovářik, Karel
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Convection dominant diffusion
Convergence
Diffusion
Double nonlinear parabolic equation
Finite element method
Finite volume method
Mathematical analysis
Mathematical models
Media
Nonlinear degenerate equation
Nonlinearity
Richards' equation
Transport contaminant in porous media
Variably saturated flow
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Summary:The combined finite volume–finite element scheme for a double nonlinear parabolic convection-dominated diffusion equation which models the variably saturated flow and contaminant transport problems in porous media is extended. Whereas the convection is approximated by a finite volume method (Multi-Point Flux Approximation), the diffusion is approximated by a finite element method. The scheme is fully implicit and involves a relaxation-regularized algorithm. Due to monotonicity and conservation properties of the approximated scheme and in view of the compactness theorem we show the convergence of the numerical scheme to the weak solution. Our scheme is applied for computing two dimensional examples with different degrees of complexity. The numerical results demonstrate that the proposed scheme gives good performance in convergence and accuracy.
ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2013.12.007