Fully Discrete Finite Element Methods for Two-Dimensional Bingham Flows

This paper presents fully discrete stabilized finite element methods for two-dimensional Bingham fluid flow based on the method of regularization. Motivated by the Brezzi-Pitkaranta stabilized finite element method, the equal-order piecewise linear finite element approximation is used for both the velocity and the pressure. Based on Euler semi-implicit scheme, a fully discrete scheme is introduced. It is shown that the proposed fully discrete stabilized finite element scheme results in the h(1/2) error order for the velocity in the discrete norms corresponding to L-2(0,T; H-1(Omega)(2)) boolean AND L-infinity(0, T; L-2(Omega)(2)).