A C0 weak Galerkin method for linear Cahn–Hilliard–Cook equation with random initial condition

2022 ◽  
Vol 414 ◽  
pp. 126659
Author(s):  
Shimin Chai ◽  
Yu Wang ◽  
Wenju Zhao ◽  
Yongkui Zou
Keyword(s):  
Galerkin Method ◽  
Random Initial Condition ◽  
Initial Condition ◽  
Weak Galerkin

scholarly journals Mixed Weak Galerkin Method for Heat Equation with Random Initial Condition

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Chenguang Zhou ◽  
Yongkui Zou ◽  
Shimin Chai ◽  
Fengshan Zhang
Keyword(s):  
Finite Element ◽  
Heat Equation ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Optimal Order ◽  
Random Initial Condition ◽  
Initial Condition ◽  
Polynomial Functions ◽  
Weak Galerkin ◽  
Convergence Estimates

This paper is devoted to the numerical analysis of weak Galerkin mixed finite element method (WGMFEM) for solving a heat equation with random initial condition. To set up the finite element spaces, we choose piecewise continuous polynomial functions of degree j+1 with j≥0 for the primary variables and piecewise discontinuous vector-valued polynomial functions of degree j for the flux ones. We further establish the stability analysis of both semidiscrete and fully discrete WGMFE schemes. In addition, we prove the optimal order convergence estimates in L2 norm for scalar solutions and triple-bar norm for vector solutions and statistical variance-type convergence estimates. Ultimately, we provide a few numerical experiments to illustrate the efficiency of the proposed schemes and theoretical analysis.

scholarly journals Existence and Uniqueness Results for Two-Dimensional Stochastic Linearised Boussinesq Equation

2020 ◽  
Vol 6 (1) ◽  
pp. 20
Author(s):  
Sofije Hoxha ◽  
Fejzi Kolaneci
Keyword(s):  
Galerkin Method ◽  
Existence And Uniqueness ◽  
Continuous Dependence ◽  
Boussinesq Equation ◽  
Initial Condition ◽  
Two Dimensional ◽  
Boussinesq Problem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Drainable Porosity

The water flow in saturated zones of the soil is described by two-dimensional Boussinesq equation. This paper is devoted to investigating the linearised stochastic Boussinesq problem in the presence of randomness in hydraulic conductivity, drainable porosity, recharge, evapotranspiration, initial condition and boundary condition. We use the Sabolev spaces and Galerkin method. Under some suitable assumptions, we prove the existence and uniqueness results, as well as, the continuous dependence on the data for the solution of linearised stochastic Boussinesq problem. Keywords: linearised stochastic Boussinesq equation, Galerkin method, existence and uniqueness results, and continuous dependence on the data.

scholarly journals A Weak Galerkin Method for the Reissner–Mindlin Plate in Primary Form

2017 ◽  
Vol 75 (2) ◽  
pp. 782-802
Author(s):  
Lin Mu ◽  
Junping Wang ◽  
Xiu Ye
Keyword(s):  
Galerkin Method ◽  
Mindlin Plate ◽  
Weak Galerkin ◽  
Primary Form

Control and Applications of Chaos

1997 ◽  
Vol 07 (10) ◽  
pp. 2175-2197 ◽  
Author(s):  
Celso Grebogi ◽  
Ying–Cheng Lai ◽  
Scott Hayes
Keyword(s):  
Feedback Control ◽  
Power Systems ◽  
System Performance ◽  
Chaotic Systems ◽  
Electrical Power ◽  
Random Initial Condition ◽  
Initial Condition ◽  
Chaotic Orbit ◽  
Electrical Power Systems ◽  
Dissipative Dynamical Systems

This review describes a procedure for stabilizing a desirable chaotic orbit embedded in a chaotic attractor of dissipative dynamical systems by using small feedback control. The key observation is that certain chaotic orbits may correspond to a desirable system performance. By carefully selecting such an orbit, and then applying small feedback control to stabilize a trajectory from a random initial condition around the target chaotic orbit, desirable system performance can be achieved. As applications, three examples are considered: (1) synchronization of chaotic systems; (2) conversion of transient chaos into sustained chaos; and (3) controlling symbolic dynamics for communication. The first and third problems are potentially relevant to communication in engineering, and the solution of the second problem can be applied to electrical power systems to avoid catastrophic events such as the voltage collapse.

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