Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Physical Sciences and Mathematics
Numerical Methods For Stochastic Stokes And Navier-Stokes Equations, Liet Vo
Numerical Methods For Stochastic Stokes And Navier-Stokes Equations, Liet Vo
Doctoral Dissertations
This dissertation consists of three main parts with each part focusing on numerical approximations of the stochastic Stokes and Navier-Stokes equations.
Part One concerns the mixed finite element methods and Chorin projection methods for solving the stochastic Stokes equations with general multiplicative noise. We propose a modified mixed finite element method for solving the Stokes equations and show that the numerical solutions converge optimally to the PDE solutions. The convergence is under energy norms (strong convergence) for the velocity and in a time-averaged norm (weak convergence) for the pressure. In addition, after establishing the error estimates in second moment, high …
Analysis Of Solvability And Applications Of Stochastic Optimal Control Problems Through Systems Of Forward-Backward Stochastic Differential Equations., Kirill Yevgenyevich Yakovlev
Analysis Of Solvability And Applications Of Stochastic Optimal Control Problems Through Systems Of Forward-Backward Stochastic Differential Equations., Kirill Yevgenyevich Yakovlev
Doctoral Dissertations
A stochastic metapopulation model is investigated. The model is motivated by a deterministic model previously presented to model the black bear population of the Great Smoky Mountains in east Tennessee. The new model involves randomness and the associated methods and results differ greatly from the deterministic analogue. A stochastic differential equation is studied and the associated results are stated and proved. Connections between a parabolic partial differential equation and a system of forward-backward stochastic differential equations is analyzed.
A "four-step" numerical scheme and a Markovian type iterative numerical scheme are implemented. Algorithms and programs in the programming languages C and …