This work concerns the analysis and finite element approximations of the evolutionary Stokes equations, with inhomogeneous boundary and divergence data. The proposed weak formulation can be viewed as an attempt to develop the parabolic analog of the well known saddle point theory for elliptic problems. Several results concerning the analysis and finite element approximations are presented. The key feature of the weak formulation under consideration is the treatment of Dirichlet boundary conditions within the Lagrange multiplier framework.
Mots-clés : Evolutionary stokes equations, inhomogeneous boundary and divergence data, error estimates, finite element approximations, lagrange multipliers, saddle point formulations
@article{M2AN_2017__51_4_1501_0,
author = {Chrysafinos, Konstantinos and Hou, L. Steven},
title = {Analysis and approximations of the evolutionary {Stokes} equations with inhomogeneous boundary and divergence data using a parabolic saddle point formulation},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1501--1526},
publisher = {EDP-Sciences},
volume = {51},
number = {4},
year = {2017},
doi = {10.1051/m2an/2016070},
mrnumber = {3702422},
zbl = {1469.76062},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an/2016070/}
}
TY - JOUR AU - Chrysafinos, Konstantinos AU - Hou, L. Steven TI - Analysis and approximations of the evolutionary Stokes equations with inhomogeneous boundary and divergence data using a parabolic saddle point formulation JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2017 SP - 1501 EP - 1526 VL - 51 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2016070/ DO - 10.1051/m2an/2016070 LA - en ID - M2AN_2017__51_4_1501_0 ER -
%0 Journal Article %A Chrysafinos, Konstantinos %A Hou, L. Steven %T Analysis and approximations of the evolutionary Stokes equations with inhomogeneous boundary and divergence data using a parabolic saddle point formulation %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2017 %P 1501-1526 %V 51 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2016070/ %R 10.1051/m2an/2016070 %G en %F M2AN_2017__51_4_1501_0
Chrysafinos, Konstantinos; Hou, L. Steven. Analysis and approximations of the evolutionary Stokes equations with inhomogeneous boundary and divergence data using a parabolic saddle point formulation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 4, pp. 1501-1526. doi : 10.1051/m2an/2016070. http://archive.numdam.org/articles/10.1051/m2an/2016070/
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