Finite-Difference Analysis for the Linear Thermoporoelasticity Problem and Its Numerical Resolution by Multigrid Methods

Abstract

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.

Keywords:

• finite-difference scheme
• multigrid
• finite-difference method

AMS Subject Classification:

• 65N55
• 65M12
• 74F10
• 74S10