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

In the present work, error indicators for the potential and elastostatic pr oblems are used in a combined fashion to implement an adaptive meshing sche me 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 s tandard one obtained from an analysis using Hermite elements. The second is a "reduced" solution obtained representing the field variables inside an e lement 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 ele ment basis, to obtain an estimate of the magnitude of the error in the nume rical solution corresponding to the Hermite elements. In this sense, it is assumed that the bigger the difference between these two solutions, the big ger the error in the original solution with Hermite elements. Since the the rmoelastic problem in its uncoupled fashion is considered, the former appro ach is applied to both problems, heat conduction and thermoelastic. Since b oth numerical solutions for each one of these problems are obtained from ju st one analysis, the computational cost of the proposed error indicators is very low. (C) 2001 Elsevier Science Ltd. All rights reserved.