# Incompressible Fluid Application

(→Theory) |
(→Theory) |
||

Line 16: | Line 16: | ||

<math> | <math> | ||

− | \partial_{t}\mathbf{u}-\nu\Delta\mathbf{u} + \mathbf{u}\cdot\nabla\mathbf{u}+\nabla p = \mathbf{f} \quad \text{in} \Omega, \quadt\in ]0,T[ | + | \partial_{t}\mathbf{u}-\nu\Delta\mathbf{u} + \mathbf{u}\cdot\nabla\mathbf{u}+\nabla p = \mathbf{f} \quad \text{in} \Omega, \quadt \text{in} ]0,T[ |

</math> | </math> |

## Revision as of 14:04, 11 December 2009

## Contents |

## General Description

ADVERTISMENT STYLE no numerical details!!! |

### Theory

The aim of this application is to solve the well known set of **Navier-Stokes** equations. The problem suffers from severe **locking** and/or **instability** using linear FEM.

**Failed to parse (unknown function\quadt): \partial_{t}\mathbf{u}-\nu\Delta\mathbf{u} + \mathbf{u}\cdot\nabla\mathbf{u}+\nabla p = \mathbf{f} \quad \text{in} \Omega, \quadt \text{in} ]0,T[ **

This application solve the the equations....
Mathematical approach to the problems.

Nothing numerical

Insert here all the references to your papers...

\qquad \qquad \qquad \qquad\quad \:\:\,\nabla\cdot\mathbf{\rho\mbox{}u} = 0 \qquad \text{in} \Omega,\qquad t\in ]0,T[

\qquad \qquad \qquad \qquad \qquad\quad\:\,\mathbf{u} = \mathbf{u_{0}} \qquad \text{in} \Omega,\qquad t=0

\qquad \qquad \qquad \qquad \qquad\quad\:\:\:\,\mathbf{u} = \mathbf{0} \qquad \text{in} \Gamma,\qquad t\in ]0,T[

### Numerical approach

All numerical details here.

This is a part quite open, depending on the application we are considering.

Every physical problem is solved defining many different ingredients. Try to be quite schematic.