Fully Discrete Finite Element Methods for Two-Dimensional Bingham Flows

Abstract EN

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-Pitkäranta 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 h1/2 error order for the velocity in the discrete norms corresponding to L2(0,T;H1(Ω)2)∩L∞(0,T;L2(Ω)2).