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August 14, 2026SIAM Journal on Numerical AnalysisOpen Access

A Surface Finite Element Scheme for a Stochastic PDE on an Evolving Curve

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Authors

PPPaola PozziBSBjörn Stinner

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Overview

Computational analysis demonstrates a stable finite element scheme for advection-diffusion on moving curves under stochastic noise, indicating robust numerical convergence for rough forcing.

Key Points

  • To develop a discrete finite element scheme and establish error bounds for stochastic advection-diffusion equations defined on evolving closed curves.
  • Formulated a variational framework suited for stochastic partial differential equations where rough noise eliminates classical time differentiability.
  • Developed a fully discrete evolving surface finite element method discretization on moving curves.
  • Conducted numerical simulations to empirically validate the generalized error estimates.
  • Generalized classical finite element error estimates to accommodate non-differentiable stochastic forcing terms on evolving geometries.
  • Confirmed theoretical convergence rates and numerical stability across discrete simulations of advection-diffusion processes.

Cite This Study

Pozzi et al. (2026) studied this question.

synapsesocial.com/papers/6a7ec69fb70b84ec8b912be1https://doi.org/10.1137/25m1774173
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