Editorials in Scientific Journals:
J. Gopalakrishnan, P. Lederer, J. Schöberl:
"A mass conserving mixed stress formulation for the Stokes equations";
arXiv.org e-Print archive,
We propose a new discretization of a mixed stress formulation of the Stokes equations. The velocity u is approximated with H(div)-conforming finite elements providing exact mass conservation. While many standard methods use H1-conforming spaces for the discrete velocity, H(div)-conformity fits the considered variational formulation in this work. A new stress-like variable σ equalling the gradient of the velocity is set within a new function space H(curldiv). New matrix-valued finite elements having continuous "normal-tangential" components are constructed to approximate functions in H(curldiv). An error analysis concludes with optimal rates of convergence for errors in u (measured in a discrete H1-norm), errors in σ (measured in L2) and the pressure p (also measured in L2). The exact mass conservation property is directly related to another structure-preservation property called pressure robustness, as shown by pressure-independent velocity error estimates. The computational cost measured in terms of interface degrees of freedom is comparable to old and new Stokes discretizations.
Created from the Publication Database of the Vienna University of Technology.