Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations

Abstract

In this project we have developed reduced basis approximations and associated a posteriori error bounds for parametrized partial differential equations. For this development to be of relevance to AFOSR applications, careful attention has to be paid to numerical analysis; computational procedures; performance assessment; and the application to non-trivial test cases. The approach is at present relevant to linear coercive and noncoercive and nonlinear elliptic equations, linear coercive and weakly noncoercive and nonlinear parabolic equations, and certain classes of linear hyperbolic equations. Applications considered include heat transfer, acoustics, elasticity, fluid dynamics, and electromagnetics.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 2010
Accession Number
ADA563403

Entities

People

  • Anthony T. Patera
  • Jan S. Hesthaven

Organizations

  • Brown University

Tags

Communities of Interest

  • Human Systems
  • Weapons Technologies

DTIC Thesaurus Topics

  • Applied Mathematics
  • Computational Fluid Dynamics
  • Computational Science
  • Computers
  • Differential Equations
  • Engineering
  • Equations
  • Fluid Dynamics
  • Integral Equations
  • Mathematics
  • Mechanical Properties
  • Mechanics
  • Numerical Analysis
  • Partial Differential Equations
  • Scattering
  • Test And Evaluation

Fields of Study

  • Mathematics

Readers

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