Numerical reliability for mixed methods applied to flow problems in porous media

Hussein Hoteit*, J. Erhel, R. Mosé, B. Philippe, Ph Ackerer

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

30 Scopus citations

Abstract

This paper is devoted to the numerical reliability and time requirements of the Mixed Finite Element (MFE) and Mixed-Hybrid Finite Element (MHFE) methods. The behavior of these methods is investigated under the influence of two factors: the mesh discretization and the medium heterogeneity. We show that, unlike the MFE, the MHFE suffers with the presence of badly shaped discretized elements. Thereat, a numerical reliability analyzing software (Aquarels) is used to detect the instability of a matrix-inversion code generated automatically by a symbolic manipulator. We also show that the spectral condition number of the algebraic systems furnished by both methods in heterogeneous media grows up linearly according to the smoothness of the hydraulic conductivity. Furthermore, it is found that the MHFE could accumulate numerical errors if large jumps in the tensor of conductivity take place. Finally, we compare running-times for both algorithms by giving various numerical experiments.

Original languageEnglish (US)
Pages (from-to)161-194
Number of pages34
JournalComputational Geosciences
Volume6
Issue number2
DOIs
StatePublished - Oct 14 2002

Keywords

  • Elliptic/parabolic problems
  • Flow in porous media
  • Functional stability
  • Mixed and mixed-hybrid methods
  • Symbolic programming

ASJC Scopus subject areas

  • Computer Science Applications
  • Computers in Earth Sciences
  • Computational Theory and Mathematics
  • Computational Mathematics

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