Geodesic
Analysis and approximations of the evolutionary Stokes equations with inhomogeneous boundary and divergence data using a parabolic saddle point formulation
Chrysafinos, Konstantinos1 ; Hou, L. Steven2
1 Department of Mathematics, School of Applied Mathematics and Physical Sciences, National Technical University of Athens, Zografou Campus, Athens 15780, Greece.
2 Department of Mathematics, Iowa State University, Ames, IA 50011, USA.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 4, pp. 1501-1526

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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.

DOI : 10.1051/m2an/2016070
Classification : 65M12, 65M60, 76D05
Keywords: Evolutionary stokes equations, inhomogeneous boundary and divergence data, error estimates, finite element approximations, lagrange multipliers, saddle point formulations

Chrysafinos, Konstantinos 1 ; Hou, L. Steven 2

1 Department of Mathematics, School of Applied Mathematics and Physical Sciences, National Technical University of Athens, Zografou Campus, Athens 15780, Greece.
2 Department of Mathematics, Iowa State University, Ames, IA 50011, USA. 
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     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},
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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

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