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HIGH MOMENT AND PATHWISE ERROR ESTIMATES FOR FULLY DISCRETE MIXED FINITE ELEMENT APPROXIMATIONS OF THE STOCHASTIC STOKES EQUATIONS WITH MULTIPLICATIVE NOISE
  • LIET VO
LIET VO
The University of Tennessee Knoxville Department of Mathematics

Corresponding Author:[email protected]

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Abstract

This paper is concerned with high moment and pathwise error estimates for both velocity and pressure approximations of the Euler-Maruyama scheme for time discretization and its two fully discrete mixed finite element discretizations. Optimal rates of convergence are established for all pth moment errors for p≥2 using a novel bootstrap technique. The almost optimal rates of convergence are then obtained using Kolmogorov’s theorem based on the high moment error estimates. Unlike for the velocity error estimate, the high moment and pathwise error estimates for the pressure approximation are proved in a time-averaged norm. In addition, the impact of noise types on the rates of convergence for both velocity and pressure approximations is also addressed. Finally, numerical experiments are also provided to validate the proven theoretical results and to examine the dependence/growth of the error constants on the moment order p.
16 Aug 2023Submitted to Mathematical Methods in the Applied Sciences
16 Aug 2023Submission Checks Completed
16 Aug 2023Assigned to Editor
23 Aug 2023Review(s) Completed, Editorial Evaluation Pending
27 Aug 2023Reviewer(s) Assigned