Finite Element Methods and Navier-Stokes Equations

accuracy application approximate solution approximation assume barycentric basis functions boundary conditions called Chapter components computed consider constant construction contains continuity equation convergence corresponding defined denotes dependent derivatives differential direct Dirichlet discretized divergence-free elimination elliptic equal equivalent error example exists expressed fact Find finite difference finite element flow fluid formulation free boundary Galerkin given gives grad Hence implies initial integration introduce iteration known linear matrix means method minimization Navier-Stokes equations necessary Neumann nodal points normal obtain parameter penalty positive possible practical pressure problem quadratic reduced reference region relation requires satisfied scheme Section shown side solution solved space Stokes equations stress Substitution surface system of equations term theorem treated triangle turbulent unique unknowns values variational vector velocity vertices written zero