Fully discrete finite element approximation of the stochastic Cahn-Hilliard-Navier-Stokes system

被引：2

作者：

Deugoue, G. ^{[1
,2
]}

Moghomye, B. Jidjou ^{[1
]}

Medjo, T. Tachim ^{[2
]}

机构：

[1] Univ Dschang, Dept Math & Comp Sci, POB 67, Dschang, Cameroon

[2] Florida Int Univ, Dept Math & Stat, MMC, Miami, FL 33199 USA

来源：

IMA JOURNAL OF NUMERICAL ANALYSIS | 2021年 / 41卷 / 04期

关键词：

stochastic Cahn-Hilliard-Navier-Stokes; weak martingale solutions; finite element method; Euler scheme; Wiener process; compactness; DIFFUSE-INTERFACE MODEL; PHASE-FIELD MODEL; ENERGY STABLE SCHEMES; SEMIDISCRETE SCHEME; INCOMPRESSIBLE FLUIDS; ERROR ANALYSIS; 2-PHASE FLOW; CONVERGENCE; MARTINGALE; SIMULATION;

D O I：

10.1093/imanum/draa056

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the numerical approximation of the stochastic Cahn-Hilliard-Navier-Stokes system on a bounded polygonal domain of R-d, d = 2, 3. We propose and analyze an algorithm based on the finite element method and a semiimplicit Euler scheme in time for a fully discretization. We prove that the proposed numerical scheme satisfies the discrete mass conservative law, has finite energies and constructs a weak martingale solution of the stochastic Cahn-Hilliard-Navier-Stokes system when the discretization step (both in time and in space) tends to zero.

引用

页码：3046 / 3112

页数：67

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