Block Iterative Methods for Elliptic Finite Element Equations.

Abstract

Direct iterative methods for solving the linear system AU = Y split A into a difference M-N. By viewing N as a weak multiplication operator, the authors determine the convergence rates of block direct iterative methods for solving the system of equations that arises in the finite element approximation of an elliptic boundary value problem. They illustrate the theory with an analysis of second order Dirichlet problems in the unit square, using Hermite cubic finite element spaces. However, the method of analysis extends to general elliptic boundary value problems of order 2m on bounded domains in d space dimensions, and to a broad class of finite element spaces.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1983
Accession Number
ADA129150

Entities

People

  • Michael Steuerwalt
  • Seymour V. Parter

Organizations

  • University of Wisconsin Madison Department of Mathematics

Tags

Communities of Interest

  • Air Platforms
  • Autonomy
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Computations
  • Convergence
  • Difference Equations
  • Differential Equations
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Finite Element Analysis
  • Inequalities
  • Linear Systems
  • Mathematics
  • Numbers
  • Operating Systems
  • Partial Differential Equations
  • Universities

Fields of Study

  • Mathematics

Readers

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

Technology Areas

  • Space