Finite Element Approximations of Stochastic Linear Schr\"{o}dinger equation driven by additive Wiener noise

Suprio Bhar; Mrinmay Biswas; Mangala Prasad

Finite Element Approximations of Stochastic Linear Schr\"{o}dinger equation driven by additive Wiener noise

Numerical Analysis 2026-01-16 v2 Numerical Analysis Mathematical Physics Analysis of PDEs math.MP Probability

Authors: Suprio Bhar , Mrinmay Biswas , Mangala Prasad

Abstract

In this article, we have analyzed semi-discrete finite element approximations of the Stochastic linear Schr\"{o}dinger equation in a bounded convex polygonal domain driven by additive Wiener noise. We use the finite element method for spatial discretization and derive an error estimate with respect to the discretization parameter of the finite element approximation. Numerical experiments have also been performed to support theoretical bounds.

Keywords

stochastic Schrödinger equation finite element method Wiener noise error estimate numerical experiments

Cite

@article{arxiv.2410.06006,
  title  = {Finite Element Approximations of Stochastic Linear Schr\"{o}dinger equation driven by additive Wiener noise},
  author = {Suprio Bhar and Mrinmay Biswas and Mangala Prasad},
  journal= {arXiv preprint arXiv:2410.06006},
  year   = {2026}
}

Comments

Theorem 2.3 and Theorem 2.4 have been updated

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