Numerical modelling of infinite domains in coupled field problems

Two- and three-field problems are often defined in domains which may be assumed as unbounded. The traditional approach for their numerical simulation, within the framework of the finite element method, is by simple truncation of the mesh at a finite boundary. This fact both results in a large number of degrees of freedom and causes often errors in the analysis, due to the difficulty of setting correct conditions at the finite boundary. This paper shows the possible errors of the ensuing numerical solution and points out the usefulness of the infinite elements to simulate the far field response. Three examples from the field of isothermal and nonisothermal consolidation are presented where the improvements in the numerical simulation obtained by the use of infinite elements are evidenced. These examples may be considered as representative for a series of other coupled problems involving partial differential equations with first order time derivatives. © 1988 Pitagora Editrice Bologna.