Nonlinear Piecewise Polynomial Approximation Beyond Besov Spaces

Abstract

We study nonlinear n-term approximation in L(sub p)(All real numbers [expn 2]) (0 < p < infinity) from Courant elements or (discontinuous) piecewise polynomials generated by multilevel nested triangulations of All real numbers (expn 2) which allow arbitrarily sharp angles. To characterize the rate of approximation we introduce and develop three families of smoothness space generated by multilevel nested triangulations. We call them B-spaces because they can be viewed as generalizations of Besov spaces. We use the B-spaces to prove Jackson and Bernstein estimates for n-term piecewise polynomial approximation and consequently characterize the corresponding approximation spaces by interpolation. We also develop methods for n-term piecewise polynomial approximation which capture the rates of the best approximation.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2001
Accession Number
ADA640673

Entities

People

  • Borislav Karaivanov
  • Pencho Petrushev

Organizations

  • University of South Carolina

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Information Operations
  • Mathematics
  • Numbers
  • Polynomials
  • Real Numbers
  • South Carolina
  • Three Dimensional
  • Triangulation

Fields of Study

  • Mathematics

Readers

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

Technology Areas

  • Space
  • Space - Orbital Debris