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

Mohammed Shuker Mahmood*, Karel Kovářik

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)11-31
Number of pages21
JournalApplied Numerical Mathematics
Publication statusPublished - 2014


  • Convection dominant diffusion
  • Double nonlinear parabolic equation
  • Finite element method
  • Finite volume method
  • Nonlinear degenerate equation
  • Richards' equation
  • Transport contaminant in porous media
  • Variably saturated flow

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis


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