New joint publication with SFB 1313 contribution, published in the scientific journal Computer Methods in Applied Mechanics and Engineering. The work has been developed in the context of the SFB 1313 research project A02.
"Mixed finite element projection methods for the unsteady Stokes equations"
Authors
- Costanza Aricò (University of Palermo)
- Rainer Helmig (University of Stuttgart, research projects A02 and C02)
- Ivan Yotov (Univerity of Pittsburgh, SFB 1313 Mercator Fellow, research project A02)
Abstract
We develop H(div)-conforming mixed finite element methods for the unsteady Stokes equations modeling single-phase incompressible fluid flow. A projection method in the framework of the incremental pressure correction methodology is applied, where a predictor and a corrector problems are sequentially solved, accounting for the viscous effects and incompressibility, respectively. The predictor problem is based on a stress-velocity mixed formulation, while the corrector projection problem uses a velocity-pressure mixed formulation. The scheme results in pointwise divergence-free velocity computed at the end of each time step. We establish unconditional stability and first order in time accuracy. In the implementation we focus on generally unstructured triangular grids. We employ a second order multipoint flux mixed finite element method based on the next-to-the-lowest order Raviart-Thomas space RT1 and a suitable quadrature rule. In the predictor problem this approach allows for a local stress elimination, resulting in element-based systems for each velocity component with three degrees of freedom per element. Similarly, in the corrector problem, the velocity is locally eliminated and an element-based system for the pressure is solved. At the end of each time step we obtain a second order accurate H(div)-conforming piecewise linear velocity, which is pointwise divergence free. We present a series of numerical tests to illustrate the performance of the method.