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

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.

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Document Details

Document Type
Technical Report
Publication Date
Dec 11, 1997
Accession Number
ADA335531

Entities

People

  • J. R. Whiteman
  • Souradet Y. Shaw

Organizations

  • Brunel University London

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Contracts
  • Displacement
  • Equations
  • Error Analysis
  • Errors
  • Finite Element Analysis
  • Integrals
  • Mathematics
  • Notation
  • Security
  • Time Intervals
  • United States
  • Universities
  • Viscoelasticity
  • Volterra Equations

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)

Technology Areas

  • Space