Title: Adaptive finite element method for wick stochastic partial differential equations

Authors: Boujemâa Achchab; Khalid Bouihat; Abderrezzak El-Bouayadi

Addresses: Laboratory of Analysis and Modeling Systems for Decision Support, Department of Mathematics Computer Engineering, ENSA, Hassan 1st University, B.P. 218, Berrechid 26100, Morocco; Mohammed VI Polytechnic University, Ben Guerir, Morocco ' Laboratory of Analysis and Modeling Systems for Decision Support, Department of Mathematics Computer Engineering, ENSA, Hassan 1st University, B.P. 218, Berrechid 26100, Morocco ' Laboratory of Analysis and Modeling Systems for Decision Support, Department of Mathematics Computer Engineering, ENSA, Hassan 1st University, B.P. 218, Berrechid 26100, Morocco

Abstract: In this paper we approximate the solution of the wick stochastic partial differential equation by the affine conforming finite element method. Then we provide a priori and a posteriori error estimations and prove the convergence of the numerical method. In particular, we construct a Galerkin approximation scheme and we derive the local residual based on posteriori error indicator, all the while proving its efficiency and reliability. Finally, two numerical examples are presented and analysed to illustrate the derived theoretical results, the effectiveness of the proposed adaptive algorithm and the good behaviour of the numerical solution and the mesh adaptation strategy used.

Keywords: wick stochastic equation? finite element method? a posteriori error estimation? error indicators? adaptive meshes.

DOI: 10.1504/IJMMNO.2023.134153

International Journal of Mathematical Modelling and Numerical Optimisation, 2023 Vol.13 No.4, pp.327 - 351

Received: 21 Nov 2022
Accepted: 30 Mar 2023
Published online: 12 Oct 2023 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article