Numerical Methods for Singularly Perturbed Differential Equations with Applications.

Abstract

During the period covered by this grant, we conducted research on the development and application of adaptive numerical methods for singularly perturbed initial-boundary value problems for partial differential equations. We studied both local refinement methods and methods of lines techniques using properly nested and overlapping grids. The geometric modeling capabilities of our procedures were improved through the use of finite quadtree and octree encoding schemes; parallel versions of adaptive procedures on shared-memory computers were developed; and variable-order finite element methods to be used with adaptive p- and hp-refinement were created.

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Document Details

Document Type
Technical Report
Publication Date
Aug 31, 1990
Accession Number
ADA235188

Entities

People

  • J. E. Flaherty

Organizations

  • Rensselaer Polytechnic Institute

Tags

Communities of Interest

  • Advanced Electronics

DTIC Thesaurus Topics

  • Applied Mathematics
  • Computational Fluid Dynamics
  • Computational Science
  • Computer Science
  • Computers
  • Differential Equations
  • Equations
  • Finite Element Analysis
  • Mathematical Analysis
  • Mathematics
  • New York
  • Parallel Computing
  • Parallel Processing
  • Partial Differential Equations
  • Trees (Data Structures)

Fields of Study

  • Mathematics

Readers

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