%0 Unpublished Work %1 Canton2015Solution %A Canton, Jacopo %A Tugnoli, M. %D 2015 %K 35b60-pdes-continuation-and-prolongation-of-solutions 65h20-global-methods-including-homotopy-approaches 76d05-incompressible-navier-stokes-equations 76m10-finite-element-methods-in-fluid-mechanics %T Solution of the Steady Navier–Stokes Equations by Newton FEM %U http://services.aero.polimi.it/\~quartape/bacheca/materiale\_didattico/NEWTON\_FEM.pdf %X This work describes a Finite Element Newton Method for the solution of the stationary Navier–Stokes equations for two-dimensional incompressible flows. We start from the weak variational formulation of the problem and adopt an unequal order interpolation \$P^1\$–\$P^2\$ for pressure and velocity. Rather general boundary conditions are considered. The Newton method for the nonlinear system of coupled equations is written in a particularly transparent incremental form and the Jacobian linear system is solved by means of a dire ct algorithm (MUMPS). The results of some numerical tests are provided to demonstrate the correctness and capability of the method.

@unpublished{Canton2015Solution, abstract = {This work describes a Finite Element Newton Method for the solution of the stationary Navier–Stokes equations for two-dimensional incompressible flows. We start from the weak variational formulation of the problem and adopt an unequal order interpolation \$\mathds{P}^1\$–\$\mathds{P}^2\$ for pressure and velocity. Rather general boundary conditions are considered. The Newton method for the nonlinear system of coupled equations is written in a particularly transparent incremental form and the Jacobian linear system is solved by means of a dire ct algorithm (MUMPS). The results of some numerical tests are provided to demonstrate the correctness and capability of the method.}, added-at = {2019-03-01T00:11:50.000+0100}, author = {Canton, Jacopo and Tugnoli, M.}, biburl = {https://www.bibsonomy.org/bibtex/256c9d90d7fa8f3cfe5063238b306a2f0/gdmcbain}, citeulike-article-id = {14414541}, citeulike-attachment-1 = {canton_15_solution.pdf; /pdf/user/gdmcbain/article/14414541/1115705/canton_15_solution.pdf; ba714f71f720327e4135ced2306e0b10ea72a3e1}, citeulike-linkout-0 = {http://services.aero.polimi.it/\~{}quartape/bacheca/materiale\_didattico/NEWTON\_FEM.pdf}, day = 14, file = {canton_15_solution.pdf}, interhash = {dbaf7afb3ba48f4d6d1410a28ccef6fb}, intrahash = {56c9d90d7fa8f3cfe5063238b306a2f0}, keywords = {35b60-pdes-continuation-and-prolongation-of-solutions 65h20-global-methods-including-homotopy-approaches 76d05-incompressible-navier-stokes-equations 76m10-finite-element-methods-in-fluid-mechanics}, month = oct, posted-at = {2017-08-16 04:15:31}, priority = {5}, timestamp = {2019-03-01T00:11:50.000+0100}, title = {Solution of the Steady {N}avier–{S}tokes Equations by {N}ewton {FEM}}, url = {http://services.aero.polimi.it/\~{}quartape/bacheca/materiale\_didattico/NEWTON\_FEM.pdf}, year = 2015 }