Adaptive meshing for two-dimensional thermoelastic problems using Hermite boundary elements

Abstract

In the present work, error indicators for the potential and elastostatic problems are used in a combined fashion to implement an adaptive meshing scheme for the solution of two-dimensional steady-state thermoelastic problems using the Boundary Element Method. These error indicators exploit in their formulation the possibility of generating two different numerical solutions from just one analysis using Hermite elements. The first solution is the standard one obtained from an analysis using Hermite elements. The second is a “reduced” solution obtained representing the field variables inside an element using some of the degrees of freedom of the Hermite element together with Lagrangian shape functions. The basic idea behind the computation of the error indicator is to compare these two solutions, on an element by element basis, to obtain an estimate of the magnitude of the error in the numerical solution corresponding to the Hermite elements. In this sense, it is assumed that the bigger the difference between these two solutions, the bigger the error in the original solution with Hermite elements. Since the thermoelastic problem in its uncoupled fashion is considered, the former approach is applied to both problems, heat conduction and thermoelastic. Since both numerical solutions for each one of these problems are obtained from just one analysis, the computational cost of the proposed error indicators is very low.