CONVERGENCE OF A DECOUPLED SPLITTING SCHEME FOR THE CAHN-HILLIARD-NAVIER-STOKES SYSTEM

被引：12

作者：

Liu, Chen ^{[1
]}

Masri, Rami ^{[2
]}

Riviere, Beatrice ^{[3
]}

机构：

[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

[2] Simula Res Lab, Dept Numer Anal & Sci Comp, N-0164 Oslo, Norway

[3] Rice Univ, Dept Computat Appl Math & Operat Res, Houston, TX 77005 USA

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2023年 / 61卷 / 06期

基金：

美国国家科学基金会;

关键词：

Cahn--Hilliard--Navier--Stokes; discontinuous Galerkin; stability; optimal error bounds; FINITE-ELEMENT APPROXIMATION; ENERGY-STABLE SCHEMES; DISCONTINUOUS GALERKIN METHODS; 2-PHASE INCOMPRESSIBLE FLOWS; ERROR ANALYSIS; 2ND-ORDER; TIME; EQUATION; SOBOLEV; MODEL;

D O I：

10.1137/22M1528069

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is devoted to the analysis of an energy-stable discontinuous Galerkin algorithm for solving the Cahn-Hilliard-Navier-Stokes equations within a decoupled splitting framework. We show that the proposed scheme is uniquely solvable and mass conservative. The energy dissipation and the L degrees stability of the order parameter are obtained under a CFL-like constraint. Optimal a priori error estimates in the broken gradient norm and in the L2 norm are derived. The stability proofs and error analysis are based on induction arguments and do not require any regularization of the potential function.

引用

收藏

页码：2651 / 2694

页数：44

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