A Moving Finite Element Method for Time Dependent Partial Differential Equations with Error Estimation and Refinement.

Abstract

The authors discuss a moving finite element method for solving vector systems of time dependent partial differential equations in one space dimension. The mesh is moved so as to equidistribute the spatial component of the discretization error in H1. They present a method of estimating this error by using p-hierarchic finite elements. The error estimate is also used in an adaptive mesh refinement procedure to give an algorithm that combines mesh movement and refinement. The authors discretize the partial differential equations in space using a Galerkin procedure with piecewise linear elements to approximate the solution and quadratic elements to estimate the error. A system of ordinary differential equations for mesh velocities are used to control element motions. The authors use existing software for stiff ordinary differential equations for the temporal integration of the solution, the error estimate, and the mesh motion. Computational results using a code based on this method are presented for several examples.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1984
Accession Number
ADA147719

Entities

People

  • J. E. Flaherty
  • S. Adjerid

Organizations

  • Rensselaer Polytechnic Institute

Tags

Communities of Interest

  • Advanced Electronics
  • C4I
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Boundaries
  • Boundary Layer
  • Command Control Communications
  • Computational Fluid Dynamics
  • Computational Science
  • Computer Science
  • Differential Equations
  • Equations
  • Finite Element Analysis
  • Fluid Dynamics
  • Fluid Mechanics
  • Mechanics
  • Partial Differential Equations
  • Payload
  • Plastic Explosives
  • Waves

Fields of Study

  • Mathematics

Readers

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

Technology Areas

  • Space