navier_stokes_mesh2d, MATLAB data files which define meshes for several 2D test problems involving the Navier Stokes equations for fluid flow, provided by Leo Rebholz.

We are interested in these meshes as useful tests for a procedure in which we are able to redo the related Navier Stokes calculations using FENICS.

As part of that task, we need to take the meshes associated with the MATLAB computation and translate them into a format acceptable to DOLFIN / FENICS. Our proposed mechanism for this is either to translate the files to the Gmsh msh format, and then use DOLFIN-CONVERT to convert that to DOLFIN XML, or else to translate the files directly into DOLFIN XML format ourselves.

The following files each contain a mesh, defined by a node coordinate list, a node index list for each element, and boundary nodes. The first line of the file lists the number of nodes, the number of elements, and the number of boundary segments.

Each node coordinate line lists the 3D coordinates of a node.

Each element line lists 3 node indices forming the element, plus an integer tag that seems to be 0 always.

Each boundary segment line lists two node indices that form a line segment along the boundary, plus an integer tag that probably is used to specify the boundary condition applied along that line.


The computer code and data files made available on this web page are distributed under the GNU LGPL license.


navier_stokes_mesh2d is available in a MATLAB version.

Related Data and Programs:

dolfin, a Python program which are used with the DOLFIN library to set up and solve a wide variety of problems using the finite element method.

dolfin-convert, a Python program which can convert mesh file from Gmsh, MEDIT, METIS or SCOTCH format to an XML format suitable for use by DOLFIN or FENICS, by Anders Logg.

dolfin_xml, a data directory which contains examples of XML files that describe 3D finite element meshes as used by DOLFIN and FENICS.

fenics, a code which illustrates the use of a collection of free software with an extensive list of features for automated, efficient solution of differential equations.

gmsh, examples which illustrate the use of the Gmsh program, a 3D mesh generator for the finite element method (FEM).

navier_stokes_2d_exact, evaluates an exact solution to the incompressible time-dependent Navier-Stokes equations over an arbitrary domain in 2D.


navier_stokes_mesh3d, MATLAB data files defining meshes for several 3D test problems involving the Navier Stokes equations for flow flow, provided by Leo Rebholz.


Leo Rebholz


  1. Abigail Bowers, Leo Rebholz, Aziz Takhirov, Catalin Trenchea,
    Improved accuracy in regularization models of incompressible flow via adaptive nonlinear filtering,
    International Journal for Numerical Methods in Fluids,
    Volume 70, Number 7, 2012, pages 805-828.

Source Code:

The following functions operate on the mesh data:

CYLINDER_2D is a mesh for 2D flow past a square cylinder, using 1649 nodes, 3078 elements, and 220 boundary nodes.

STEP_2D is a mesh for 2D flow past a forward and backward step, using 537 nodes, 960 elements, and 112 boundary nodes.

Last revised on 21 February 2019.