Application Of The Sensitivity Analysis Of An Error Estimator To The Generation Of An Adaptive Remeshing Strategy
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This work proposes a new adaptive remeshing strategy based on the sensitivity of the point wise error in stresses with respect to the nodal coordinates, which is computed using the adjoint-state method. This sensitivity provides information about the influence of the discretization of each zone of the computational domain in the estimation of the error in stresses at a specific point. This information is also used for the development of an adaptive remeshing strategy that provides a strict and economical control of this error. Keywords: adaptive remeshing, error estimator, sensitivity analysis. 1 Introduction In the solid mechanics context, the idea of improving the mesh quality by using a sensitivity analysis is not new. The first historical reference comes from McNeic and Marcal , who proposed to improve a mesh by minimizing the potential energy of the structural problem with respect to the nodal coordinates. Another important reference comes from Kang et al. , who maximized the deformation energy with respect to the nodal coordinates. These works allow a mesh with a fixed topology to be optimized. On the other hand, it is possible to obtain specific adaptive remeshing strategies for the control of the point wise error of any physical quantity related with the structural analysis (see Bugeda ), but the control of the pollution error (see Babuška et al. [4, 5]) obligates to control the local error everywhere, this producing globally adapted meshes with a very high number of degrees of freedom. Nevertheless, when doing a structural analysis we know very often
adaptive remeshing, error estimator, sensitivity analysis.