P-2014-28
C. Carstensen, B.D. Reddy, M. Schedensack
A Natural Nonconforming FEM for the Bingham Flow Problem is Quasi-Optimal
Abstract: This paper introduces a novel three-field formulation for the Bingham flow problem and the relative named after Mosolov and low-order discretizations: a nonconforming for the classical formulation and a mixed finite element method for the three-field model. The two discretizations are equivalent and quasi-optimal in the sense that the H1 error of the primal variable is bounded by the error of the L2 bestapproximation
of the stress variable. This improves the predicted convergence rate by a log factor of the maximal mesh-size in comparison to the first-order conforming finite element method in a model scenario. Despite that numerical experiments lead to comparable results, the nonconforming scheme is proven to be quasi-optimal while this is not guaranteed for the conforming one.
Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2014-28
MSC 2000: 65N30, 76M10
33 pp.