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Mixed finite elements and Newton‐type linearizations for the solution of Richards' equation
Author(s) -
Bergamaschi Luca,
Putti Mario
Publication year - 1999
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19990720)45:8<1025::aid-nme615>3.0.co;2-g
Subject(s) - mathematics , discretization , polygon mesh , finite element method , newton's method , convergence (economics) , mathematical analysis , nonlinear system , geometry , physics , quantum mechanics , economics , thermodynamics , economic growth
We present the development of a two‐dimensional Mixed‐Hybrid Finite Element (MHFE) model for the solution of the non‐linear equation of variably saturated flow in groundwater on unstructured triangular meshes. By this approach the Darcy velocity is approximated using lowest‐order Raviart–Thomas (RT 0 ) elements and is ‘exactly’ mass conserving. Hybridization is used to overcome the ill‐conditioning of the mixed system. The scheme is globally first‐order in space. Nevertheless, numerical results employing non‐uniform meshes show second‐order accuracy of the pressure head and normal fluxes on specific grid points. The non‐linear systems of algebraic equations resulting from the MHFE discretization are solved using Picard or Newton iterations. Realistic sample tests show that the MHFE‐Newton approach achieves fast convergence in many situations, in particular, when a good initial guess is provided by either the Picard scheme or relaxation techniques. Copyright © 1999 John Wiley & Sons, Ltd.