FINITE ELEMENT METHOD FOR STOKES EQUATIONS UNDER LEAK BOUNDARY CONDITION OF FRICTION TYPE?

摘要

Stokes equations are considered with the leak boundary condition of friction type. We propose a discrete variational inequality based on one of the P1/P1-stabilized, P1b/P1, and P2/P1 finite elements. We show that a suitable numerical-integration approximation for the nonlinear term preserves in a discrete sense some properties known in continuous problems. Those properties are essential to justify our error estimate and numerical implementation in a consistent way. Numerical examples are presented to confirm the theoretical results.