Nested finite element approximation of parabolic SPDEs with Whittle-Mat\'ern noise
<|reference_start|>Nested finite element approximation of parabolic SPDEs with Whittle-Mat\'ern noise: We propose a new type of fully discrete finite element approximation of a class of semilinear stochastic parabolic equations with additive noise. Our discretization differs from the ones typically considered, in that we employ a nested finite element approximation of the noise. This is well suited for dealing with covariance operators defined in terms of (negative powers of) elliptic operators, like that of Whittle-Mat\'ern random fields. We derive strong and pathwise convergence rates for our proposed discretization, and our results are supported by numerical experiments.<|reference_end|>
@article{auestad2024nested,
    title={Nested finite element approximation of parabolic SPDEs with
  Whittle-Mat\'ern noise},
    author={{O}yvind Stormark Auestad},
    journal={arXiv preprint arXiv:2406.11041},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.11041},
    primaryClass={math.NA cs.NA}
}