Volume 51, Number 4, July-August 2017
|Page(s)||1501 - 1526|
|Published online||10 August 2017|
Analysis and approximations of the evolutionary Stokes equations with inhomogeneous boundary and divergence data using a parabolic saddle point formulation
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.
Received: 23 June 2015
Revised: 21 October 2016
Accepted: 9 November 2016
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.
Mathematics Subject Classification: 65M12 / 65M60 / 76D05
Key words: Evolutionary stokes equations / inhomogeneous boundary and divergence data / error estimates / finite element approximations / lagrange multipliers / saddle point formulations
© EDP Sciences, SMAI 2017
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