Space-time approximation of stochastic $p$-Laplace systems

Dominic Breit; Martina Hofmanova; Sebastien Loisel

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arXiv · 1904.03134

Space-time approximation of stochastic $p$-Laplace systems

Dominic Breit·Martina Hofmanova·Sebastien Loisel

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Abstract

We consider systems of stochastic evolutionary equations of the $p$-Laplace type. We establish convergence rates for a finite-element based space-time approximation, where the error is measured in a suitable quasi-norm. Under natural regularity assumptions on the solution, our main result provides linear convergence in space and convergence of order $α$ in time for all $α\in(0,\frac{1}{2})$. The key ingredient of our analysis is a random time-grid, which allows us to compensate for the lack of time regularity. Our theoretical results are confirmed by numerical experiments.

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Dominic Breit, Martina Hofmanova, Sebastien Loisel. 2021-05-07. Space-time approximation of stochastic $p$-Laplace systems. https://arxiv.org/abs/1904.03134

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