Adaptive Refinement Methods for Nonlinear Parabolic Partial Differential Equations.

Abstract

This document considers two adaptive finite element techniques for parabolic partial differential equations (PDEs) that are based on using error estimates to control mesh refinement. One technique is a method of lines approach that uses a Galerkin method to discretize the PDEs in space and implicit multi-step integration in time. Spatial elements are added and deleted in regions of high and low error and are all advanced with the same sequence of varying time steps. The second technique is a local refinement method that uses Galerkin approximations in both space and time. Fine grids of space-time elements are added to coarser grids and the problem is recursively solved in regions of high error. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1984
Accession Number
ADA160314

Entities

People

  • J. E. Flaherty
  • M. Bietermman
  • P. K. Moore

Organizations

  • Rensselaer Polytechnic Institute

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Computational Fluid Dynamics
  • Computational Science
  • Computations
  • Computer Science
  • Computers
  • Differential Equations
  • Engineering
  • Equations
  • Estimators
  • Galerkin Method
  • Lists (Data Structures)
  • Partial Differential Equations
  • Pattern Recognition
  • Recognition
  • Sequences

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Computational Fluid Dynamics (CFD)
  • Fluid Dynamics.

Technology Areas

  • Space