P. Lederer:

"A Mass Conserving Mixed Stress Formulation For Incompressible Flows";

Supervisor, Reviewer: J. Schöberl, J. Gopalakrishnan, R. Stenberg; Institut für Analysis und Scientific Computing, 2019; oral examination: 2019-03-20.

This work deals with the introduction and the analysis of a new ﬁnite element method for the discretization of incompressible ﬂows. The main focus essentially lies on the discussion of the linear incompressible Stokes equations. These equations describe the physical behaviour and the relation - derived from the fundamental Newtonian laws - between the ﬂuid velocity and the pressure (-gradient). Where the standard variational formulation of the Stokes equations demand a Sobolev regularity of order one for the velocity, we give an answer to the question if it is possible to deﬁne a variational formulation demanding a weaker regularity property of the velocity.

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