Solution Manifolds and Submanifolds of Parametrized Equations and Their Discretization Errors.

Abstract

The paper concerns solution manifolds of nonlinear parameter-dependent equations (1) F(u,lambda) = y sub o involving a Fredholm operator F between (infinite-dimensional) Banach spaces X = Z x lambda and Y, and a finite-dimensional parameter space lambda. Differential-geometric ideas are used to discuss the connection between augmented equations and certain one-dimensional submanifolds produced by numerical path-tracing procedures. Then, for arbitrary (finite) dimension of lambda, estimates of the error between the solution manifold of (1) and its discretizations are developed. These estimates are shown to be applicable to rather general nonlinear boundary-value problems for partial differential equations. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1983
Accession Number
ADA130186

Entities

People

  • James P. Fink
  • Werner Rheinboldt

Organizations

  • University of Pittsburgh

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Air Force
  • Banach Space
  • Boundaries
  • Boundary Value Problems
  • Computational Science
  • Convergence
  • Differential Equations
  • Differential Geometry
  • Equations
  • Functional Analysis
  • Hilbert Space
  • Integrals
  • Mathematics
  • Navier Stokes Equations
  • Partial Differential Equations
  • Sequences
  • Stability Conditions

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Linear Algebra

Technology Areas

  • Space