Accession Number : ADA335531

Title :   Robust Adaptive Finite Element Schemes for Nonlinear Viscoelastic Solid Deformation: An Investigative Study

Descriptive Note : Interim rept. 11 Sep-11 Dec 97

Corporate Author : BRUNEL UNIV UXBRIDGE (UNITED KINGDOM)

Personal Author(s) : Whiteman, J. R. ; Shaw, S.

PDF Url : ADA335531

Report Date : 11 DEC 1997

Pagination or Media Count : 5

Abstract : In this first three month phase of the research project we have continued our existing work, as outlined in the original Seed Project Proposal, on the numerical solution of quasistatic viscoelasticity problems. These space-time problems have been modelled using hereditary integral constitutive relations, and we have produced a priori and a posteriori energy-norm error estimates for space-time finite element discretizations for the linear quasistatic problem. The basic a posteriori (i.e. calculable) error estimate allows for adaptive in space mesh refinement but, due to a lack of strong temporal stability in the underlying problem, not for adaptive time stepping. In order to address this difficulty we have developed a posteriori error bounds in less physical (weaker) norms which do allow adaptive time step control. This appears to be the first time that such error control is possible for second kind Volterra equations.

Descriptors :   *ADAPTIVE CONTROL SYSTEMS, *FINITE ELEMENT ANALYSIS, *DEFORMATION, *VISCOELASTICITY, *SOLIDS, *NONLINEAR ANALYSIS, NUMERICAL ANALYSIS, ESTIMATES, ERRORS, VOLTERRA EQUATIONS, UNITED KINGDOM.

Subject Categories : Numerical Mathematics
      Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE