Applications of Adaptive Finite Element Methods to Problems in Estimation and Control for Partial Differential Equations

Abstract

The purpose of this grant has been to undertake research in the general area of adaptive-grid finite element methods in estimation and control problems. The overall goal has been to investigate adaptive gridding numerical algorithms and to develop a solid theory to handle the mathematical questions of convergence and stability which arise in the use of such algorithms. The P.I. has met this goal through the study of a number of adaptive-grid finite element methods for parameter estimation problems governed by distributed parameter systems. In addition, stability problems encountered in the implementation of such algorithm have led her to make extensive studies of the ill-posed nature of these problems. In particular, theoretical and numerical studies were undertaken concerning regularization schemes for a number of ill-posed estimation problems. Specific applications considered in this latter study include the inverse heat conduction problem and regularizing aspects of descent methods as used to minimize fit-to-data functions associated with linear estimation problems.

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Document Details

Document Type
Technical Report
Publication Date
Jul 14, 1991
Accession Number
ADA244052

Entities

People

  • Patricia A. Lamm

Organizations

  • Michigan State University

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Differential Equations
  • Equations
  • Finite Element Analysis
  • Inverse Problems
  • Mathematical Analysis
  • Mathematics
  • Michigan
  • North Carolina
  • Partial Differential Equations
  • Symposia
  • Universities

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Computational Fluid Dynamics (CFD)
  • Theoretical Analysis.