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Error estimation and adaptive meshing in strongly nonlinear dynamic problems

Radovitzky, R. and Ortiz, M. (1999) Error estimation and adaptive meshing in strongly nonlinear dynamic problems. Computer Methods in Applied Mechanics and Engineering, 172 (1-4). pp. 203-240. ISSN 0045-7825. doi:10.1016/S0045-7825(98)00230-8.

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We present work aimed at developing a general framework for mesh adaption in strongly nonlinear, possibly dynamic, problems. We begin by showing that the solutions of the incremental boundary value problem for a wide class of materials, including nonlinear elastic materials, compressible Newtonian fluids and viscoplastic solids, obey a minimum principle, provided that the constitutive updates are formulated appropriately. This minimum principle can be 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. We demonstrate the robustness and versatility of the computational framework with the aid of convergence studies and selected examples of application.

Item Type:Article
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Ortiz, M.0000-0001-5877-4824
Additional Information:© 1999 Elsevier. Received 4 May 1998. The support of the Sandia National Laboratories through contract DE-AC04-76DP00789, and of the Army Research Office through contract DAAH04-96-1-0056, is gratefully acknowledged.
Funding AgencyGrant Number
Department of Energy (DOE)DE-AC04-76DP00789
Army Research Office (ARO)DAAH04-96-1-0056
Issue or Number:1-4
Record Number:CaltechAUTHORS:20171213-090926881
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Official Citation:R. Radovitzky, M. Ortiz, Error estimation and adaptive meshing in strongly nonlinear dynamic problems, In Computer Methods in Applied Mechanics and Engineering, Volume 172, Issues 1–4, 1999, Pages 203-240, ISSN 0045-7825, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83859
Deposited By: Lydia Suarez
Deposited On:13 Dec 2017 23:06
Last Modified:15 Nov 2021 20:14

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