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PreprintarXiv licencearXiv

An Immersed Interface Method for Parabolic Interface Problems with Nonlinear Jump Conditions

  • So-Hsiang Chou
  • Patrick Nyadjo Fonga
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Abstract

We develop an immersed interface finite difference method for a one-dimensional nonlinear parabolic interface problem with jump condition [u]α=λu+u-. The method combines a Crank--Nicolson immersed interface discretization with an s-parameter reduction of the nonlinear interface condition, thereby reducing the nonlinear coupling to a scalar quadratic equation. We also discuss two different viewpoints for combining Newton iteration with immersed interface discretization, namely the IIM--Newton and Newton--IIM formulations. Numerical experiments are presented to illustrate the behavior and accuracy of the method.

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Cite

BibTeXRIS
BibTeX
@misc{chou2026immersed,
  title = {{An Immersed Interface Method for Parabolic Interface Problems with Nonlinear Jump Conditions}},
  author = {So-Hsiang Chou and Patrick Nyadjo Fonga},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.30062},
  eprint = {2608.30062},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.30062},
}
RIS
TY  - UNPB
TI  - An Immersed Interface Method for Parabolic Interface Problems with Nonlinear Jump Conditions
AU  - So-Hsiang Chou
AU  - Patrick Nyadjo Fonga
PY  - 2026
DA  - 2026/08/30
PB  - arXiv
DO  - 10.48550/arxiv.2608.30062
UR  - https://arxiv.org/abs/2608.30062
AB  - We develop an immersed interface finite difference method for a one-dimensional nonlinear parabolic interface problem with jump condition [u]_α=λu^+u^-. The method combines a Crank--Nicolson immersed interface discretization with an s-parameter reduction of the nonlinear interface condition, thereby reducing the nonlinear coupling to a scalar quadratic equation. We also discuss two different viewpoints for combining Newton iteration with immersed interface discretization, namely the IIM--Newton and Newton--IIM formulations. Numerical experiments are presented to illustrate the behavior and accuracy of the method.
ER  -