Application of 3d goal-oriented mesh adaptivity for model error estimation of a specific quantity
Seyed Shahram Ghorashi, Timon Rabczuk
Bauhaus-Universitaet Weimar, Germany
None of mathematical models and numerical simulations can predict exactly a physical phenomenon. They can only approximate it by applying some assumptions. Selection of models and simulations can be based on the required accuracy and affordable computational cost. Existing error in final results can be categorized in two main parts: Model error and discretization errors. Different types of error estimation have been developed for estimating the discretization error. The conventional error estimation approaches estimates the error in energy norm. Since in engineering applications specific quantities, e.g. displacement at a point or average stresses in a small region, are of interest, a new generation of error estimation called Goal-oriented error estimation has been developed. In this contribution a goal-oriented error estimation methodology entitled Dual-weighted residual is further extended for estimating the error of a quantity in three-dimensional elastoplastic problems. The resulted elementwise errors are applied for mesh-adaptivity purpose. By defining a maximum permissible error for the prescribed quantity, the mesh adaptivity procedure is performed whenever it is needed. Therefore, the result of the specific quantity is computed based on the required accuracy. In order to estimate the model error, a model needs to be considered as a reference model, since the exact model does not exist. Then, by applying the proposed approach for the reference model and an interest model, the result of prescribed quantity can be obtained by minimizing the discretization error. As a result, their subtraction gives the model error of the quantity. Finally, a cantiliver beam which is made of Aluminium in rectangular tube shape is analyzed and model error of displacement at the free end is computed.
ISSN 1611 - 4086 | © IKM 2015