Relaxation model for the p-Laplacian problem with stiffness

Heesun Choi, Hongjoong Kim, Marc Laforest

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

This paper proposes a new numerical scheme in 1-D for the p-Laplacian problem for the electromagnetic effects in a high-temperature Type II superconductors. The scheme is obtained by applying a relaxation approximation to the nonlinear derivatives in the problem. The new relaxation scheme achieves highly accurate results even for large p that makes the p-Laplacian flux stiff. The scheme is novel in that it is high-order accurate and predicts physically correct non-oscillatory magnetic fronts within these conductors, the later of which is not found by finite element approximate solutions done by the engineering community. The work is an extension of previous work on relaxation schemes applied to degenerate parabolic problems. Numerical tests are presented to validate the performance of the new scheme.

Original languageEnglish
Pages (from-to)173-189
Number of pages17
JournalJournal of Computational and Applied Mathematics
Volume344
DOIs
Publication statusPublished - 2018 Dec 15

Keywords

  • Degenerate parabolic
  • Hyperbolic system
  • Power-law model
  • Relaxation scheme
  • Superconductivity
  • p-Laplacian

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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