Abstract
This paper analyses the numerical difficulties commonly encountered in solving fully coupled numerical models and proposes a numerical strategy apt to overcome them. The proposed procedure is based on space refinement and time adaptivity. The latter, which in mainly studied here, is based on the use of a finite element approach in the space domain and a Discontinuous Galerkin approximation within each time span. Error measures are defined for the jump of the solution at each time station. These constitute the parameters allowing for the time adaptivity. Some care is however, needed for a useful definition of the jump measures. Numerical tests are presented firstly to demonstrate the advantages and shortcomings of the method over the more traditional use of finite differences in time, then to assess the efficiency of the proposed procedure for adapting the time step. The proposed method reveals its efficiency and simplicity to adapt the time step in the solution of coupled field problems.
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Simoni, L., Secchi, S. & Schrefler, B.A. Numerical difficulties and computational procedures for thermo-hydro-mechanical coupled problems of saturated porous media. Comput Mech 43, 179–189 (2008). https://doi.org/10.1007/s00466-008-0302-2
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DOI: https://doi.org/10.1007/s00466-008-0302-2