Well-posedness and H(div)-conforming finite element approximation of a linearised model for inviscid incompressible flow

被引：6

作者：

Barrenechea, Gabriel ^{[1
]}

Burman, Erik ^{[2
]}

Guzman, Johnny ^{[3
]}

机构：

[1] Univ Strathclyde, Dept Math & Stat, 26 Richmond St, Glasgow G1 1XH, Lanark, Scotland

[2] UCL, Dept Math, London WC1E 6BT, England

[3] Brown Univ, Div Appl Math, Box F 182 George St, Providence, RI 02912 USA

来源：

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | 2020年 / 30卷 / 05期

基金：

英国工程与自然科学研究理事会; 美国国家科学基金会;

关键词：

Inviscid flows; well-posedness; H(div)-conforming finite elements; error estimates; DISCONTINUOUS GALERKIN METHOD; STOKES; DISCRETIZATION; CONVERGENCE;

D O I：

10.1142/S0218202520500165

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a linearised model of incompressible inviscid flow. Using a regularisation based on the Hodge Laplacian we prove existence and uniqueness of weak solutions for smooth domains. The model problem is then discretised using H(div)-conforming finite element methods, for which we prove error estimates for the velocity approximation in the L-2-norm of order O(h(k+1/2)). We also prove error estimates for the pressure error in the L-2-norm.

引用

页码：847 / 865

页数：19

共 50 条

[41] Well-posedness theory of an inhomogeneous traffic flow model
Li, T
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2002, 2 (03): : 401 - 414
[42] Well-Posedness and Finite Element Approximation for the Stationary Magneto-Hydrodynamics Problem with Temperature-Dependent Parameters
Hailong Qiu
Journal of Scientific Computing, 2020, 85
[43] Well-Posedness and Finite Element Approximation for the Stationary Magneto-Hydrodynamics Problem with Temperature-Dependent Parameters
Qiu, Hailong
JOURNAL OF SCIENTIFIC COMPUTING, 2020, 85 (03)
[44] Well-posedness of first-order acoustic wave equations and space-time finite element approximation
Fuehrer, Thomas
Gonzalez, Roberto
Karkulik, Michael
IMA JOURNAL OF NUMERICAL ANALYSIS, 2025,
[45] Convergence Analysis of H(div)-Conforming Finite Element Methods for a Nonlinear Poroelasticity Problem
Zeng, Yuping
Weng, Zhifeng
Liang, Fen
DISCRETE DYNAMICS IN NATURE AND SOCIETY, 2020, 2020
[46] Positive and non-positive solutions for an inviscid dyadic model: well-posedness and regularity
Barbato, David
Morandin, Francesco
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2013, 20 (03): : 1105 - 1123
[47] Global well-posedness and large time behavior for the inviscid Oldroyd-B model
Ye, Weikui
Zhao, Bin
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2024, 79
[48] A TOXIN-MEDIATED SIZE-STRUCTURED POPULATION MODEL: FINITE DIFFERENCE APPROXIMATION AND WELL-POSEDNESS
Huang, Qihua
Wang, Hao
MATHEMATICAL BIOSCIENCES AND ENGINEERING, 2016, 13 (04) : 697 - 722
[49] Stability, well-posedness and blow-up criterion for the Incompressible Slice Model
Alonso-Oran, Diego
de Leon, Aythami Bethencourt
PHYSICA D-NONLINEAR PHENOMENA, 2019, 392 : 99 - 118
[50] Positive and non-positive solutions for an inviscid dyadic model: well-posedness and regularity
David Barbato
Francesco Morandin
Nonlinear Differential Equations and Applications NoDEA, 2013, 20 : 1105 - 1123

← 1 2 3 4 5 →