A quasi-variational inequalar problem in superconductivar

John W. Barrett, Leonid Prigozhin, J. Ball

Research output: Contribution to journalArticlepeer-review

32 Scopus citations

Abstract

We derive a class of analytical solutions and a dual formulation of a scalar two-space-dimensional quasi-variational inequal-AR problem in applied superconductiv-AR. We approximate this formulation by a fully practical finite element method based on the lowest order RaviartThomas element, which yields approximations to both the primal and dual variables (the magnetic and electric fields). We prove the subsequence convergence of this approximation, and hence prove the existence of a solution to both the dual and primal formulations, for strictly star-shaped domains. The effectiveness of the approximation is illustrated by numerical examples with and without this domain restriction.

Original languageEnglish
Pages (from-to)679-706
Number of pages28
JournalMathematical Models and Methods in Applied Sciences
Volume20
Issue number5
DOIs
StatePublished - 1 May 2010

Keywords

  • Convergence analysis
  • Critical-state problems
  • Existence
  • Finite elements
  • Kim model
  • Mixed methods
  • Quasi-variational inequalities
  • Superconductivity

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