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PreprintCC BY-NC-ND 4.0arXiv

Super-approximation and optimal L2 convergence of the stabilized BGN method with piecewise linear parametric finite elements for curve-shortening flow

  • Genming Bai
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Abstract

We develop a bihomotopy argument to estimate the discrete material time derivatives of consistency functionals. Combined with summation-by-parts, this argument yields a directional super-convergence estimate for the consistency contribution when tested with the normal error velocity. Together with the super-approximation of the reversely weighted discrete normal, these techniques establish Lt∞ Hx1 super-convergence of the projection error and optimal Lt∞ Lx2 convergence of the trajectory error of a stabilized BGN method for curve-shortening flow with piecewise linear parametric finite elements.

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Cite

BibTeXRIS
BibTeX
@misc{bai2026superapproximation,
  title = {{Super-approximation and optimal $L^2$ convergence of the stabilized BGN method with piecewise linear parametric finite elements for curve-shortening flow}},
  author = {Genming Bai},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.23326},
  eprint = {2609.23326},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.23326},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Super-approximation and optimal L^2 convergence of the stabilized BGN method with piecewise linear parametric finite elements for curve-shortening flow
AU  - Genming Bai
PY  - 2026
DA  - 2026/09/20
PB  - arXiv
DO  - 10.48550/arxiv.2609.23326
UR  - https://arxiv.org/abs/2609.23326
AB  - We develop a bihomotopy argument to estimate the discrete material time derivatives of consistency functionals. Combined with summation-by-parts, this argument yields a directional super-convergence estimate for the consistency contribution when tested with the normal error velocity. Together with the super-approximation of the reversely weighted discrete normal, these techniques establish L_t^∞ H_x^1 super-convergence of the projection error and optimal L_t^∞ L_x^2 convergence of the trajectory error of a stabilized BGN method for curve-shortening flow with piecewise linear parametric finite elements.
ER  -