A Posteriori Error Estimates for Parametrized Nonlinear Equations

Abstract

A new approach to the construction of a posteriori error estimates for finite element solutions of multiparameter nonlinear problems presented. The estimates are derived from local, element-by-element solutions of linearizations of the problems; they turn out to be very effective, computationally rather inexpensive, and insensitive to the choice of the local coordinate system on the solution manifold. Frequently, in practical computations in engineering and science, the aim is to obtain results which are sufficiently accurate and reliable to allow for a decision about the physical system under study. A posteriori error estimates play a very important role in achieving this aim. Such estimates are needed not only for judging the reliability of the computed results but also for controlling adaptive processes designed to achieve desired error tolerances at minimal cost or best possible solutions within allowable cost ranges. (KR)

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1990
Accession Number
ADA224067

Entities

People

  • Jinn-lian Liu
  • Werner Rheinboldt

Organizations

  • University of Pittsburgh

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Banach Space
  • Boundaries
  • Boundary Value Problems
  • Computations
  • Coordinate Systems
  • Differential Equations
  • Equations
  • Finite Element Analysis
  • Hilbert Space
  • Mathematics
  • New York
  • Numerical Analysis
  • Partial Differential Equations
  • Stability Conditions
  • Structural Mechanics
  • Theorems

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Systems Analysis and Design