Space-time approximation of stochastic p-Laplace type systems

Dominic Breit, Martina Hofmanová, Sebastien Loisel

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Abstract

We consider systems of stochastic evolutionary equations of 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 (almost) 1/2 in time. 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.
Original languageEnglish
Pages (from-to)2218–2236
Number of pages19
JournalSIAM Journal on Numerical Analysis
Volume59
Issue number4
DOIs
Publication statusPublished - 12 Aug 2021

Keywords

  • Finite element methods
  • Nonlinear Laplace-type systems
  • Parabolic stochastic PDEs
  • Space-time discretization

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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