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

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