Space-time approximation of stochastic p-Laplace systems

2019/04/05 by Dominic Breit, Martina Hofmanová, Breit, Dominic +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Approximation and Integration #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1904.03134

openalex publication_date 2019/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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∈(0,(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.

Citations

• Galerkin Finite Element Methods for Stochastic Parabolic Partial Differential Equations
• Parabolic Systems with Polynomial Growth and Regularity

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