An Upwind Finite Element Scheme for the Navier-Stokes Equations and its Domain Decomposition Algorithm

General Introduction / p1 1 Mixed Finite Element Method for the Navier-Stokes Equations / p5 　1.1 Introduction / p5 　1.2 Variational principle and the finite element method / p6 　1.3 Standard mixed finite element method for the Navier-Stokes equations with iso-P2 P1/P1 elements / p10 　1.4 Consistent discretized pressure Poisson equation / p15 　1.5 Decomposition into sub-tetrahedra / p17 　1.6 Conclusion / p20 2 Upwind Finite Element Scheme Based on the Choice of Up-and Down-wind Points / p21 　2.1 Introduction / p21 　2.2 Upwind finite element approximation based on the choice of up-and down-wind points / p23 　2.3 Search algorithm for the upwind points / p27 　2.4 Finite element scheme based on the choice of up-and downwind points for the Navier-Stokes equations / p34 　2.5 Stability regions with respect to α and т / p35 　2.6 Numerical results / p40 　2.7 Conclusion / p57 3 Domain Decomposition Algorithm / p58 　3.1 Introduction / p58 　3.2 Two data types for data on the nodal points / p60 　3.3 Mortar element method / p66 　3.4 Domain decomposition algorithm for the upwind finite element scheme / p73 　3.5 Conclusion / p84 General Conclusion / p85 Bibliography / p88