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.
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页码：847 / 865
页数：19
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