Discontinuos Petrov-Galerkin Methods in Banach Spaces

Abstract

Following Muga and van der Zee [8], we generalize the standard Discontinuous Petrov-Galerkin method, based on Hilbert spaces, to Banach spaces. Numerical experiments using model 1D convection- dominated diffusion problem are performed and compared with Hilbert setting. It is shown that Banach-based method gives solutions less susceptible to Gibbs phenomenon. h-adaptiviy is implemented with the help of the error representation function as error indicator.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 2019
Accession Number
AD1115624

Entities

People

  • Jiaqi Li
  • Leszek F. Demkowicz

Organizations

  • University of Texas at Austin

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Banach Space
  • Boundaries
  • Boundary Layer
  • Boundary Value Problems
  • Computations
  • Convection
  • Diffusion
  • Diffusion Coefficient
  • Equations
  • Functional Analysis
  • Galerkin Method
  • Hilbert Space
  • Layers
  • Linear Systems
  • Nonlinear Systems
  • Optimization
  • Polynomials
  • Residuals
  • Standards

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Linear Algebra
  • Quantum spin resonance or Electron Paramagnetic Resonance spectroscopy.

Technology Areas

  • Space