Numerical Reliability and CPU Time for the Mixed Methods applied to Flow Problems in Porous Media

Hussein Hoteit (1) , Jocelyne Erhel (1) , Robert Mosé (2) , Bernard Philippe (1) , Philippe Ackerer (2)

1 ALADIN - Algorithms Adapted to Intensive Numerical Computing
2 IMFS - Institut de Mécanique des Fluides et des Solides

This work 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 flatted triangular elements. A numerical reliability analyzing software (Aquarels) is used to detect the instability of the matrix-inversion code generated by MAPLE which is used in the MHFE code. 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 the conductivity varies abruptly in space. Finally, we compare running-times for both algorithms by giving various numerical experiments.

Mots clés: ELLIPTIC/PARABOLIC PROBLEMS; FLOW IN POROUS MEDIA; MIXED AND MIXED-HYBRID METHODS; FUNCTIONAL STABILITY; SYMBOLIC PROGRAMMING

Domaines: Autre [cs.OH]

Hussein Hoteit, Jocelyne Erhel, Robert Mosé, Bernard Philippe, Philippe Ackerer. Numerical Reliability and CPU Time for the Mixed Methods applied to Flow Problems in Porous Media. [Research Report] RR-4228, INRIA. 2001. ⟨inria-00072391⟩