Abstract
AbstractThe numerical analysis of stochastic parabolic partial differential equations of the form $$\begin{aligned} du + A(u)\, dt = f \,dt + g \, dW, \end{aligned}$$
d
u
+
A
(
u
)
d
t
=
f
d
t
+
g
d
W
,
is surveyed, where A is a nonlinear partial operator and W a Brownian motion. This manuscript unifies much of the theory developed over the last decade into a cohesive framework which integrates techniques for the approximation of deterministic partial differential equations with methods for the approximation of stochastic ordinary differential equations. The manuscript is intended to be accessible to audiences versed in either of these disciplines, and examples are presented to illustrate the applicability of the theory.
Funder
Czech Science foundation
National Science Foundation
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Modeling and Simulation,Statistics and Probability
Reference41 articles.
1. Baňas, L., Brzeźniak, Z., Neklyudov, M., Prohl, A.: Stochastic ferromagnetism, volume 58 of De Gruyter Studies in Mathematics. De Gruyter, Berlin (2014). Analysis and numerics
2. Billingsley, P.: Convergence of Probability Measures. Wiley Series in Probability and Statistics: Probability and Statistics, 2nd edn. Wiley, New York (1999)
3. Brenner, S., Scott, R.: The Mathematical Theory of Finite Element Methods. Texts in Applied Mathematics, vol. 15. Springer, Berlin (2008)
4. Brezzi, F., Fortin, M.: Mixed and Hybrid Finite Element Methods. Number 15 in Computational Mathematics. Springer, Berlin (1991)
5. Brzeźniak, Z., Carelli, E., Prohl, A.: Finite-element-based discretizations of the incompressible Navier–Stokes equations with multiplicative random forcing. IMA J. Numer. Anal. 33(3), 771–824 (2013)
Cited by
5 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献