This paper deals with the numerical solution of a two-dimensional thermoporoelasticity problem using a finite-difference scheme. Two issues are discussed: stability and convergence in discrete energy norms of the finite-difference scheme are proved, and secondly, a distributive smoother is examined in order to find a robust and efficient multigrid solver for the corresponding system of equations. Numerical experiments confirm the convergence properties of the proposed scheme, as well as fast multigrid convergence.
Boal, N., Gaspar, F. J., Lisbona, F., & Vabishchevich, P. (2012). Finite-difference analysis for the linear thermoporoelasticity problem and its numerical resolution by multigrid methods. Mathematical Modelling and Analysis, 17(2), 227-244. https://doi.org/10.3846/13926292.2012.662177
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