navier_stokes_mesh3d, MATLAB data files which define meshes for several 3D 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 computer code and data files made available on this web page are distributed under the MIT license


navier_stokes_mesh3d is available in a MATLAB version.

Related Data and Programs:

dolfin, a Python program which uses 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 illustrate 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_3d_exact, evaluates an exact solution to the incompressible time-dependent Navier-Stokes equations over an arbitrary domain in 3D.

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


tet_mesh_order20, a dataset directory which contains examples of order 20 tetrahedral meshes.

tet_mesh_to_gmsh, a MATLAB code which reads information defining a tet mesh, namely a file of node coordinates and a file of elements defined by node indices, and creates a corresponding Gmsh mesh file.


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 MAT files each contain a mesh, defined by a structure whose components are nodeco, elnode, and bdynde:

The following functions operate on the mesh data:

Last revised on 22 February 2019.