Error estimation and adaptivity in elastodynamics
The authors try to apply mesh adaptive techniques to elastodynamics. There are few papers concerning the problem of mesh adaptation for hyperbolic problems. This paper summarizes the recent works of the authors. The excellent introduction gives the reader the view to mesh adaptation techniques and error estimation. Both spatial and temporal discretization is considered. \(h\) and \(p\) version of adaptive techniques are presented with references to the most characteristic literature contributions. Error analysis proves the lower error order for time discretization than for space one. That is why only error indicator related to spatial variables is significant for mesh modification. The mesh is modified according to the error distribution in spatial domain. Since the phenomenon observed changes in time, the mesh is also changed in each several steps of time integration of the differential equation of motion. The mesh regeneration is performed with the use of the smoothed field of characteristic parameters of the problem (for example, stress). Nodal parameters are transferred between two different meshes in that way. However, the error introduced by this procedure is not considered or evaluated. For vibration analysis, regeneration of the mesh with different geometry may be difficult provided the smoothing procedure is applied both to space and time. Such a discussion could eliminate doubts in individual applications. Examples of eigenvalue analysis and direct integration of the motion equation demonstrate the efficiency of the approach. It allows to reduce the number of variables in the problem and finally decrease the computational effort. Although the problem of mesh adaptation in elastodynamics is still open, the paper can be interesting for people working in the domain of applications of computer methods to structural dynamics.
scientific article; zbMATH DE number 429036
scientific article