Error estimation and adaptive meshing in strongly nonlinear dynamic problems

Citation

Radovitzky, Raul A (1998) Error estimation and adaptive meshing in strongly nonlinear dynamic problems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/MF7F-YK03. https://resolver.caltech.edu/CaltechETD:etd-11032003-113427

Abstract

This dissertation is concerned with the development of a general computational framework for mesh adaption such as is required in the three-dimensional lagrangian finite element simulation of strongly nonlinear, possibly dynamic, problems. It is shown that, for a very general constitutive framework, the solutions of the incremental boundary value problem obey a minimum principle, provided that the constitutive updates are formulated appropriately. This minimum principle is taken as a basis for asymptotic error estimation. In particular, we chose to monitor the error of a lower-order projection of the finite element solution. The optimal mesh size distribution then follows from a posteriori error indicators which are purely local, i. e., can be computed element-by-element.

A sine qua non condition for the successful accomplishment of the kind of analysis envisioned in this work is the possibility to mesh the deforming domains of analysis. In the first section of this thesis a method is presented for mesh generation in complex geometries and general--possibly non-manifold--topologies.

The robustness and versatility of the computational framework is demonstrated with the aid of convergence studies and selected examples of application and the results contrasted with previous approaches

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