A Galerkin Method on Nonlinear Subsets and Its Application to a Singular Perturbation Problem.

Abstract

In the Ritz-Galerkin method, the linear subspace of the trial solutions is extended to a closed subset. As an example, a class of so-called sublinear approximation and interpolation is developed. Some results, such as orthogonalization and minimum property of the error function, are obtained. A second order scheme has been developed for solving a linear singular perturbation elliptic problem. Error estimates are given for a uniform mesh size. For the same accuracy, the present nonlinear scheme is one order of magnitude more than the usual method used in the piecewise linear subspace. Numerical results for the linear and semi-linear singular perturbation problems are included.

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Document Details

Document Type
Technical Report
Publication Date
Jun 23, 1982
Accession Number
ADA121570

Entities

People

  • Jiachang Sun

Organizations

  • Yale University

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Boundaries
  • Boundary Layer
  • Boundary Value Problems
  • Computational Fluid Dynamics
  • Computational Science
  • Differential Equations
  • Equations
  • Errors
  • Fluid Dynamics
  • Galerkin Method
  • Interpolation
  • Layers
  • Linear Systems
  • Polynomials
  • Precision
  • Sequences

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Mathematical Modeling and Probability Theory.