Numerical Methods for Singularly Perturbed Differential Equations with Applications

Abstract

During the three-year period of this project, we conducted research on the development, analysis, and application of serial and parallel adaptive computational strategies for solving transient and steady partial differential systems. Concentrating on high-order methods and adaptive approaches that combine mesh refinement and coarsening (h-refinement, order variation (p- refinement), and occasionally, mesh motion (r-refinement), we addressed problems in combustion, materials science and compressible fluid mechanics. Special spatially-discrete finite element Galerkin methods were considered for the parallel and adaptive solution of hyperbolic conservation laws. Improved solution-limiting and error-estimation strategies increased the accuracy and efficiency of these methods which are being applied to two - and three- dimensional compressible flow problems. Adaptive techniques for dissipative systems are being applied to problems in the manufacture of ceramic composite media.

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Document Details

Document Type
Technical Report
Publication Date
Mar 31, 1993
Accession Number
ADA272112

Entities

People

  • J. E. Flaherty

Organizations

  • Rensselaer Polytechnic Institute

Tags

Communities of Interest

  • Advanced Electronics
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Boundary Layer
  • Ceramic Matrix Composites
  • Computational Fluid Dynamics
  • Computational Science
  • Computer Science
  • Differential Equations
  • Equations
  • Flow
  • Fluid Flow
  • Fluid Mechanics
  • Materials
  • Materials Science
  • Mathematics
  • Mechanics
  • Numerical Analysis
  • Parallel Computing
  • Three Dimensional

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Technical Research and Report Writing.