Approximate and Low Regularity Dirichlet Boundary Conditions in the Generalized Finite Element Method

Abstract

We propose a method for treating the Dirichlet boundary conditions in the framework of the Generalized Finite Element Method (GFEM). We are especially interested in boundary data with low regularity (possibly a distribution). We use approximate Dirichlet boundary conditions as in [11] and polynomial approximations of the boundary. Our sequence of GFEMspaces considered, S , = 1, 2, . . . is such that S not subset H1(sub 0) (omega), and hence it does not conform to one of the basic FEM conditions. Let h be the typical size of the elements defining S and let epilson H(exp(m+1)(omega) be the solution of the Poisson problem Deltau = f in omega , u = 0 on derivative omega , on a smooth, bounded domain omega.

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Document Details

Document Type
Technical Report
Publication Date
Jul 31, 2006
Accession Number
ADA455650

Entities

People

  • Ivo Babuška
  • Nicolae Tarfulea
  • Victor Nistor

Organizations

  • University of Texas at Austin

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Banach Space
  • Boundaries
  • Boundary Value Problems
  • Construction
  • Diameters
  • Differential Equations
  • Equations
  • Finite Element Analysis
  • Inequalities
  • Information Operations
  • Linear Systems
  • Numbers
  • Polynomials
  • Sequences
  • Theorems
  • Variational Equations

Readers

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