A Physically Motivated Domain Decomposition for Singularly Perturbed Equations

Abstract

A domain decomposition algorithm suitable for the efficient and accurate solution of a parabolic reaction convection diffusion equation with small parameter on the diffusion term is presented. Convergence is established via maximum principle arguments. The equation arises in the modeling of laminar transonic flow. Decomposition into subdomains is accomplished via singular perturbation analysis which dictates regions where certain reduced equations may be solved in place of the full equation, effectively preconditioning the problem. This paper concentrates on the theoretical basis of the method, establishing local and global a priori error bounds.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1988
Accession Number
ADA203244

Entities

People

  • Jeffrey S. Scroggs

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Boundary Layer
  • Computational Fluid Dynamics
  • Computational Science
  • Computations
  • Contracts
  • Coordinate Systems
  • Decomposition
  • Differential Equations
  • Diffusion
  • Equations
  • Flow
  • Fluid Mechanics
  • New York
  • Numerical Analysis
  • Theorems
  • Transonic Flow

Fields of Study

  • Mathematics

Readers

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