A Mixed Finite Element Formulation for the Boundary Controllability of the Wave Equation

Abstract

This paper introduces the mixed finite element method as a viable numerical procedure for the boundary controllability of the linear wave equation. Another numerical implementation using Galerkin finite elements has been investigated. However, due to approximation problems of the normal derivative on the boundary, the method becomes unstable as the mesh is refined. To correct for the ill-posedness of the approximate problem, a Tychonoff regularization method was implemented. The aforementioned paper also presents other possible remedies; among them is the mixed finite element method. The fixed finite element approximation is a plausible procedure to overcome these difficulties since the derivative at certain nodal values arises naturally from the formulation.

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Document Details

Document Type
Technical Report
Publication Date
Oct 31, 1990
Accession Number
ADA226066

Entities

People

  • M. F. Wheeler
  • R. Glowinski
  • W. Kinton

Organizations

  • University of Houston

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Boundaries
  • Boundary Value Problems
  • Computational Fluid Dynamics
  • Computational Science
  • Differential Equations
  • Engineering
  • Equations
  • Finite Element Analysis
  • Formulas (Mathematics)
  • Grids
  • Inverse Problems
  • Mathematics
  • Parallel Computing
  • Partial Differential Equations
  • Wave Equations

Fields of Study

  • Mathematics

Readers

  • Control Systems Engineering.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)