An HP-Adaptive Method in Space and Time for Parabolic Systems.

Abstract

We describe an adaptive method-of-lines hp-refinement algorithm in space and time for one-dimensional vector systems of parabolic partial differential equations. Solutions are calculated using Galerkin's method with a piecewise-polynomial hierarchical basis in space and singly-implicit Runge-Kutta (SIRK) methods in time. A posteriori estimates of the local spatial and temporal discretization error are used with a priori error estimates to control spatial and temporal enrichment. Computational results are used to compare and verify the utility of several variants of the basic hp-refinement procedure.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1993
Accession Number
ADA290453

Entities

People

  • J. E. Flaherty
  • Peter K. Moore

Organizations

  • Rensselaer Polytechnic Institute

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Accuracy
  • Air Force
  • Algorithms
  • Computations
  • Differential Equations
  • Equations
  • Extrapolation
  • Linear Systems
  • Nonlinear Systems
  • Partial Differential Equations
  • Pattern Recognition
  • Phase Transformations
  • Polynomials
  • Shear Bands
  • Shear Modulus
  • Three Dimensional

Fields of Study

  • Mathematics

Readers

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

Technology Areas

  • Space