Accession Number:

ADA224067

Title:

A Posteriori Error Estimates for Parametrized Nonlinear Equations

Descriptive Note:

Technical rept.

Corporate Author:

PITTSBURGH UNIV PA INST FOR COMPUTATIONAL MATHEMATICS AND APPLICATIONS

Personal Author(s):

• Rheinboldt, Werner C.
• Liu, Jinn-Lian

Report Date:

1990-06-01

Pagination or Media Count:

18.0

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

Descriptors:

• *ESTIMATES
• *NONLINEAR ALGEBRAIC EQUATIONS
• *ERROR ANALYSIS
• SENSITIVITY
• PROBLEM SOLVING
• COSTS
• RELIABILITY
• NONLINEAR SYSTEMS
• SOLUTIONS(GENERAL)
• COORDINATES
• ERRORS
• TOLERANCE
• ADAPTIVE SYSTEMS
• MANIFOLDS(ENGINES)
• FINITE ELEMENT ANALYSIS
• PHYSICAL PROPERTIES
• COMPUTATIONS
• PARAMETERS

Subject Categories:

• Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE