A new error indicator based on stresses for adaptive meshing with Hermite boundary elements

摘要

This work presents a new error indicator for adaptive meshing with Hermite boundary elements. The error indicator proposed here directly measures, in an approximate fashion, the error in the numerical solution for the stresses. The basic idea behind the error indicator is to compare, on an element by element basis, a solution for the stresses obtained with Hermite elements with a second, "reduced" solution. This "reduced" solution is obtained approximating the fied variables inside each element using Lagrangian shape functions together with the moda values for the displacements and traction's that were obtain from the analysis with Hermite elements. In this sense, it is assumed that the bigger the difference between the two solutions, the bigger therefor in the numerical solution for the stresses corresponding to the model with Hermit elements. Since in the scheme presented here both numeric solutions are obtained from the same analysis, the cost associated with the computation of he error indicator is minimal. Due to its simplicity and reliability, this new error indicator is very convenient to ead adaptive processes. Furthermore, it can also be used in models with multiple subregions.